Answers
Where:
P(t): percentage of initial remaining
t: time elapsed
h: half life of substance
Given the variables we know, we can solve for P(t).
[tex]P(t)=0.5^{\frac{100}{1599}}[/tex]Plugging this into a calculator, we get that
P(t) = 0.95757733 = 95.757733% remaining
Related Questions
If a convex lens (converging) has a focal length of 12 cm, where would you place an object in order to produce an image that has the same height, but inverted?Less than 12 cm6 cm12 cm24 cm
Answers
Given that the focal length is F = 12 cm.
We need to find the position of the object such that the image obtained should be inverted, the same height as that of the object.
In a convex lens, for the image to be inverted and the same height as the object, it should be placed at 2F.
So, the object position will be
[tex]\begin{gathered} 2F=2\times12 \\ =24\text{ cm} \end{gathered}[/tex]Thus, the object position should be 24 cm.
(a). Please check and calculate the average value of time in each trial.(b). It says Make a distance vs. time line graph below using the average times in Data Table 1. You will need to make sureto include a title and labeled X and Y-axis with units.(c). Make a velocity vs. time line graph below using the average velocities in Data Table 2. You will need to makesure to include a title and labeled X and Y-axis with units.
Answers
(a). For the 10 yd distance, the value of time in each trial is,
1.89 s, 1.83 s, and 1.72 s
The average value of time for 10 yd distance is,
[tex]\begin{gathered} t_1=\frac{1.89+1.83+1.72}{3} \\ t_1=1.81\text{ s} \end{gathered}[/tex]Thus, the average time for 10 yd is 1.81 seconds.
For 20 yd distance, the value of time in each trial is,
3.12 s, 3.28 s, and 3.47 s
The average value of time for 20 yd is,
[tex]\begin{gathered} t_2=\frac{3.12+3.28+3.47}{3} \\ t_2=3.29\text{ s} \end{gathered}[/tex]Thus, the average time for 20 yd is 3.29 seconds.
For 30 yd distance, the value of time in each trial is,
5.55 s, 5.14 s, and 4.44 s
The average value of time for 30 yd is,
[tex]\begin{gathered} t_3=\frac{5.55+5.14+4.44}{3} \\ t_3=5.04_{}\text{ s} \end{gathered}[/tex]Thus, the average time for 30 yd is 5.04 seconds.
For 40 yd distance, the value of time for each trial is,
7.16 s, 7.24 s, and 6.78 s
The average value of time for 40 yd is,
[tex]\begin{gathered} t_4=\frac{7.16+7.24+6.78}{3} \\ t_4=7.06\text{ s} \end{gathered}[/tex]Thus, the average value of time for 40 yd is 7.06 seconds.
A series circuit has more than one path for the electric current to follow true or false
Answers
Answer:
False, because a series circuit is one loop.
As the boat in which he is riding approaches a dock at 3.0 m/s, Jasper stands up in the boat and jumps toward the dock. Jasper applies an average force of 800. newtons on the boat for 0.30 seconds as he jumps.a. How much momentum does Jasper’s 80.-kilogram body have as it lands on the dock?b. What is Jasper's speed on the dock?
Answers
a) Take into account that the force can be written as follow:
[tex]F=\frac{\Delta p}{\Delta t}[/tex]where F is the force, Δp the change in the momentum and Δt the time interval in which the force is applied.
Moreover, consider that the change in the momentum can be written as follow:
[tex]\Delta p=m\Delta v[/tex]where m is the mass and Δv is the change in the velocity.
By replacing the previous expression into the formula for the force F, you can solve for Δv to determine the change in the velocity of Jamper due the force he applies to the boat:
[tex]\begin{gathered} F=\frac{m\Delta v}{\Delta t} \\ \Delta v=\frac{\Delta t\cdot F}{m} \end{gathered}[/tex]In this case, m=80.0kg, Δt = 0.30s and F = 800.0N.
Then, for the change in the speed you obtain:
[tex]\Delta v=\frac{0.30s\cdot800.0N}{80.0kg}=3.0\frac{m}{s}[/tex]It means that related to the boat (where you can consider that Jasper is at rest) the speed of Jasper is 3m/s. However, it is necessary to take into account the speed of the boat before Jasper jumps to the dock, which is 3.0m/s.
The speed of Jasper when he lands on the dock is then:
3.0m/s + 3.0m/s = 6.0m/s
The momentum is the product of mass and speed, then, the momentum of jasper is:
p = (80.0kg)(6.0m/s) = 480.0kg*m/s
b) Based on the previous calculations, you have that the Jasper's speed on the dock is 6.0m/s
Which of the following terms best describes the luminosity of the sun?A. WattageB. TemperatureC. DistanceD. Energy
Answers
The luminosity is a measure of the electromagnetic power of a source of light, therefore, its unit of measure is "Watts". Therefore, the term that best describes the luminosity of the sun is "Wattage".
What is the period of the wave?
2.5 seconds
0.4 cycles/second (hertz)
3.9 cm
1.6 cm/s
Answers
Answer:
2.5 seconds
Explanation:
Perios is time divided by number of oscilliations. From the diagram the number of oscilliations is two. This can be seen by counting successive crests of the wave from the 0s mark. The 2 oscilliatoions ends in 5s. 5 divided by 2 is 2.5s.
An oxygen atom has the mass of 2.66×10 to the -20/3 G and a glass of water has a mass of 0.050 kg. equation is in the picture
Answers
The number of moles of oxygen atoms that have a mass equal to the mass of a glass of water = 3.1 moles
Explanations:The mass of oxygen atom = The mass of glass water = 0.050kg
[tex]\begin{gathered} \text{Mass of oxygen atom = 0.050 }\times\text{ 1000g} \\ \text{Mass of oxygen atom = }50\text{ g} \end{gathered}[/tex]Use the formula below to calculate the number of moles of oxygen atoms
[tex]\text{Number of moles = }\frac{Mass\text{ in gram}}{\text{Molar mass}}[/tex]Molar mass of oxygen = 16 g/mol
Mass of oxygen atom = 50g
Substitute these values into the formula above
[tex]\begin{gathered} \text{Number of moles = }\frac{50}{16} \\ \text{Number of moles = }3.1\text{ moles} \end{gathered}[/tex]The number of moles of oxygen atoms that have a mass equal to the mass of a glass of water = 3.1 moles
A PVC pipe has a length of 53.594 centimeters.a. What are the frequencies of the first three harmonics when the pipe is open at both ends? b. What are the frequencies of the first three harmonics when the pipe is closed at one end and open at the other?
Answers
Given:
Length of pipe, L = 53.594 cm
Let's solve for the following:
• (a). What are the frequencies of the first three harmonics when the pipe is open at both ends?
To find the frequency of the first harmonics, apply the formula:
[tex]f_1=\frac{v}{2l}[/tex]Where:
v is the speed of sound = 343 m/s
l is the length of the pipe in meters.
Where:
100 cm = 1 m
53.594 cm = 0.53594 m
Hence, for the frequency, we have:
[tex]\begin{gathered} f_1=\frac{343}{2*0.53594} \\ \\ f_1=319.99\approx320\text{ Hz} \end{gathered}[/tex]For the frequency of the second harmonics, we have:
[tex]\begin{gathered} f_2=2f_1 \\ \\ f_2=2*320 \\ \\ f_2=640\text{ Hz} \end{gathered}[/tex]For the frequency of the third harmonics:
[tex]\begin{gathered} f_3=3f_1 \\ \\ f_3=3*320 \\ \\ f_3=960\text{ Hz} \end{gathered}[/tex]• Part B.
,• What are the frequencies of the first three harmonics when the pipe is closed at one end and open at the other?
For the first harmonics when the pipe is closed at one end, apply the one end open harmonics equation.
[tex]\begin{gathered} f_1=\frac{v}{4l} \\ \\ f_1=\frac{343}{4*0.53594} \\ \\ f_1=160\text{ Hz.} \end{gathered}[/tex]The next 2 harmonics will be the odd multiples of the first.
Hence, we have:
[tex]\begin{gathered} f_3=3f_1 \\ f_3=3*160 \\ f_3=480\text{ Hz.} \\ \\ \\ f_5=5f1 \\ f_5=5*160 \\ f_5=800\text{ Hz.} \end{gathered}[/tex]Therefore, the frequencies of of the first three harmonics when the pipe is closed at one end and open at the other are:
160 Hz, 480 Hz, 800 Hz.
ANSWER:
(A). 320Hz, 640 Hz, 960 Hz.
(B). 160 Hz, 480 Hz, 800 Hz.
The force of attraction between m1 and m2 is 76 N. What will this force become if m2 is tripled?
Answers
The new force is obtained as 228 N since the product of the masses is directly proportional to the force.
What is the new force?From the Newton law of universal gravitation, we can see that the gravitational force that exists between two masses is directly proportional to the product of the masses and inversely proportional to the distance between the masses.
Where the distance between the masses, remain the same, we can see that the new force would be three times the initial force since the the force and the mass are directly proportional.
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A woman holds a makeup mirror with a radius of curvature of 120 cm a distance of 20 cm from her face. What is the magnification of the observed image?
Answers
Given:
The radius of curvature is R = -120 cm
The object distance is u = -20 cm
Required: Magnification of the observed image.
Explanation:
The focal length can be calculated using the concave mirror as
[tex]\begin{gathered} f=\frac{R}{2} \\ =\frac{-120}{2} \\ =-60\text{ cm} \end{gathered}[/tex]The image distance can be calculated using the mirror formula as
[tex]\begin{gathered} \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ \frac{1}{v}=\frac{1}{f}-\frac{1}{u} \\ =\frac{1}{-60}-\frac{1}{-20} \\ v=30\text{ cm} \end{gathered}[/tex]The
You are moving a dresser that has a mass of 36 kg; its acceleration is 0.5 m/s2. What is the force being applied?72 N18 N4.8 N35.5 N
Answers
ANSWER
18 N
EXPLANATION
Given:
• The dresser's mass, m = 36 kg
,• The dresser's acceleration, a = 0.5 m/s²
Find:
• The applied force, F
By Newton's second law of motion, the net force acting on an object is equal to the product between the object's mass and its acceleration,
[tex]F=ma[/tex]Assuming that there is no friction between the dresser and the floor,
[tex]F=36kg\cdot0.5m/s^2=18N[/tex]Hence, the force being applied is 18 N.
A diver shines a flashlight upward from beneath the water (n=1.33) at an angle of 40.0° to the vertical. At what angle does the light refract through the air above the surface of the water?
Answers
Given:
The refractive index of water, n₁=1.33
The angle of incidence, θ₂=40.0°
To find:
The angle of refraction.
Explanation:
The refractive index of the air is n₂=1
From the snell's law,
[tex]n_1\sin\theta_1=n_2\sin\theta_2[/tex]Where θ₂ is the angle of refraction.
On substituting the known values,
[tex]\begin{gathered} 1.33\sin40.0\degree=1\sin\theta_2 \\ \implies\theta_2=sin^{-1}(\frac{1.33\sin40.0\degree}{1}) \\ =58.75\degree \end{gathered}[/tex]Final answer:
The angle of refraction is 58.75°
How much lift force will it take to accelerate a 10,000 Kg helicopter upward at a rate of 3 m/s2?
Answers
The amount of force required to lift the helicopter of mass 10000 kg moving with an acceleration of 3 m/s² is 30000 N.
What is force?Force is the product of mass and acceleration.
To calculate the amount of force it will take to lift the helicopter, we use the formula below.
Formula:
F = ma............. EquationWhere:
F = Force required to lift the helicopterm = Mass of the helicoptera = Acceleration of the helicopterFrom the question,
Given:
m = 10000 kga = 3 m/s²Substitute these values into equation 1
F = 10000×3F = 30000 NHence, the amount of force required to lift the helicopter is 30000 N.
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To the correct number of significant figures: 2999 - 0.1 =
Answers
ANSWER:
2999, 4 significant figures
STEP-BY-STEP EXPLANATION:
We have the following:
[tex]\begin{gathered} 2999-0.1=2998.9 \\ 2998.9\cong2999\rightarrow Decimals\colon0 \end{gathered}[/tex]Therefore, we can determine that in total there are 4 significant figures
The specific heat capacity of steel is 450 J/kg°C. If heat is added to 2 kg of steel for 30seconds, raising its temperature from 10°C to 32°C, what is the heat flow rate? Express your answer in W.
Answers
Given:
The specific heat capacity of steel is
[tex]c=\text{ 450 J/kg }^{\circ}C[/tex]The mass of the steel is m = 2 kg
The initial temperature of steel is
[tex]T_i=\text{ 10}^{\circ}\text{ C}[/tex]The final temperature of steel is
[tex]T_f\text{ = 32}^{\circ}C[/tex]
The time is t = 30 s
To find the heat flow rate.
Explanation:
The heat flow rate can be calculated by the formula
[tex]\frac{Q}{t}=\frac{mc(T_f-T_i)}{t}[/tex]On substituting the value, the heat flow rate will be
[tex]\begin{gathered} \frac{Q}{t}=\text{ }\frac{2\times450\times(32-10)}{30} \\ =\text{ 660 W} \end{gathered}[/tex]Thus, the heat flow rate is 660 W.
Question 8 of 25In a nuclear reactor, what type of a reaction provides the power?O A. FusionB. Controlled fissionC. RedoxO D. Uncontrolled fusionSUBMIT
Answers
Given:
Reaction in the nuclear reactor.
To find:
Type of nuclear reaction in the nuclear reactor that provides power.
Explanation:
In a fusion reaction, two nuclei are fused together to form a heavier nucleus. The energy released in the process is known as fusion energy. The nuclear reactors we are using today are not based on nuclear fusion reactions. Thus option A is incorrect.
Redox reaction is a chemical reaction and is not used in nuclear reactors. Thus, option C is the incorrect option.
In a nuclear fission reaction, the nuclear of an atom is bombarded with neutrons to split the nucleus into two or more two smaller nuclei which are known as daughter nuclei. During this process, a large amount of energy is released and it is known as nuclear fission energy. The nuclear technology that we used today, uses nuclear fusion reactions in the reactors. The reaction is controlled by using control rods. Thus the correct option is option B.
Final answer:
In a nuclear reactor, a controlled fusion reaction provides the power. Thus, the correct option is option B.
It takes 30 seconds for a pumpkin to roll 25 meters from rest after it is pushed withforce of 12 Newtons. What is the mass of the pumpkin?
Answers
The velocity of pumpkin can be given as,
[tex]v=\frac{d}{t}[/tex]Plug in the known values,
[tex]\begin{gathered} v=\frac{25\text{ m}}{30\text{ s}} \\ =0.833\text{ m/s} \end{gathered}[/tex]The final velocity of pumpkin can be expressed as,
[tex]v=u+at[/tex]Substitute the known values,
[tex]\begin{gathered} 0.833\text{ m/s=0 m/s+a(30 s)} \\ a=\frac{0.833\text{ m/s}}{30\text{ s}} \\ \approx0.028m/s^2 \end{gathered}[/tex]The mass of pumpkin can be given as,
[tex]m=\frac{F}{a}[/tex]Plug in the known values,
[tex]\begin{gathered} m=\frac{12\text{ N}}{0.028m/s^2}(\frac{1kgm/s^2}{1\text{ N}}) \\ \approx428.6\text{ kg} \end{gathered}[/tex]Thus, the mass of pumpking is 428.6 kg.
if the fundamental frequency of an 80 cm long guitar string is 450 Hz, what is the speed of the traveling waves?
Answers
Given that the frequency of the wave is, f = 450 Hz
and the length of the guitar string is, L = 80 cm = 0.8 m
We have to find the speed of the wave, v.
As the frequency is the fundamental frequency, so it will be the first harmonic.
The formula to find the wavelength is
[tex]\lambda=2L[/tex]Substituting the values, we get
[tex]\begin{gathered} \lambda=2\times0.8 \\ =1.6\text{ m} \end{gathered}[/tex]The formula to find the speed of the traveling wave is
[tex]v=\lambda\times f[/tex]Substituting the values, we get
[tex]\begin{gathered} v=1.6\times450 \\ =720\text{ m/s} \end{gathered}[/tex]Thus, the speed of the traveling wave is 720 m/s
A tennis ball undergoes an elastic collision when it hits the ground and bounces up. It is given that the speed of the ball justbefore it hits the ground is - v0 and immediately after rebounding it is +v0. Which of the statements below is true?Select one:O a. The momentum of the ball does not change but the momentum of Earth changes.O b. The momentum of the ball changes but the momentum of Earth does not.O c. The momentum of the ball changes and the momentum of Earth also changes by the same amount.O d. Neither the momentum of the ball nor the momentum of Earth changes.O e. Additional information is needed to answer this question.
Answers
c. The momentum of the ball changes and the momentum of Earth also changes by the same amount.
In 1897,J.J Thompson would gain recognition for discovering the electron and would later win a noble prize for his ________ model of the atom?
Answers
Plum pudding
Explanation:Note these points:
• J.J Thompson performed the Cathose ray experiment
,• From this experiment, he discovered that all atoms contain tiny negatively charged subatomic particles called electrons
,• J.J Thompson proposed the plum pudding model of the atom
,• This model contained negatively-charged electrons embedded within a positively charged soup
,• It was on April 30, 1897 that J.J Thompson announced the presence of the electrons in the atom, a result of his cathode ray experiment
From the points highlighted above, we can conclude that J.J Thompson gained recognition fpr discovering the electron and also won a noble prize for his plum pudding model of the atom
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An electric fan is plugged into an outlet and the circuit completed, making the fan blades spin. Which of the following correctly describes this situation?
A. Electrical energy is transformed into mechanical energy
B. Electrical energy is destroyed, and mechanical energy is created.
C. Mechanical energy is destroyed, and electrical energy is created
D. Mechanical energy is transformed into electrical energy
Answers
Answer:
The Correct Answer Is A.
A dog must be at least 17 pounds to enter the dog park.Which description best represents the weight the dog needs to be?Any value less than or equal to 17Any value equal to 17Any value greater than 17Any value greater than or equal to 17
Answers
ANSWER:
4th option: Any value greater than or equal to 17
STEP-BY-STEP EXPLANATION:
According to the statement, the first must be at least 17 pounds to enter the dog park, which means that the minimum weight is 17 pounds.
Which means the best way to represent it is any value greater than or equal to 17.
If you swing an object on a string around in a circle, how can you feel the effects of the centripetal force?(1 point)
A in the mass of the object
B in the length of the string
C in the tension in the string
D in the speed of the object
Answers
The effects of the centripetal force is felt in the tension in the string.
option C is the correct answer.
What is centripetal force?
Centripetal force is the inward or radial force experienced by an object moving in a circular path.
Mathematically, the centripetal force experienced by an object moving in a circular path is given as;
F = ma
where;
m is the mass of the objecta is the centripetal accelerationF = mv²/r
where;
m is the mass of the objectv is the velocity of the objectr is the radius of the circular pathThe centripetal force on the object is measured in Newton and it is equal to the tension in the string.
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Answer:
C in the tension in the string
Explanation:
At the top of a raised platform, a ball is thrown vertically upward with a speed of 60 m/s. The ball rises up, then falls to the ground below the platform with a downward speed of 90 m/s.(a) For how much time was the ball in free-fall?(b) How far is the platform from the ground?
Answers
Before we begin to answer the question we need to notice that since the gravitaional acceleration will act on the motion this is a uniform accelerated motion. This means that we can use the following equations:
[tex]g=\frac{v_f-v_0}{t}[/tex][tex]y=y_0+v_0t+\frac{1}{2}gt^2[/tex][tex]v^2_f-v^2_0=2g(y-y_0)[/tex]Before we begin we establish that upward is the positve direction, this means that g=-10 m/s^2 and that the velocity of the ball when it reaches the ground below the platform is -90 m/s. We also establis that the origin of motion is at the platform
a)
To determine the time the ball is free-falling we need to know the maximum height the ball reaches before it begins falling.
-Motion from the platform to the maximum height.
In this case the initial velocity is 60 m/s while the final velocity is 0 m/s; furthermore the initial height is zero since our origin is on the platform.
The height it reaches the ball before it starts to fall can be obtained by the third equation:
[tex]\begin{gathered} 0^2-60^2=2(-10)(y-0) \\ -3600=-20y \\ y=-\frac{3600}{20} \\ y=180 \end{gathered}[/tex]Therefore the maximum height is 180 meters.
Now the time it takes the ball to reaches this height is given by the first formula:
[tex]\begin{gathered} -10=\frac{0-60}{t} \\ t=\frac{-60}{-10} \\ t=6 \end{gathered}[/tex]Hence it takes the ball six seconds to reach its maximum height.
Now, we know that in an accelerated uniform motion the time it takes to reach the maximum height is the same as the tame it takes to reach the initial height, therefore it takes 6 seconds for the ball to travel from the maximum height to the platform again.
Now we need to determine the time it takes the ball to fall from the height of the platform to the bottom; in this case the initial velocity is -60 m/s; this comes from the fact that the final velocity is the same at same heights in this kind of motion. Then, using the first formula we know that the time it takes is:
[tex]\begin{gathered} -10=\frac{-90-(-60)}{t} \\ t=\frac{-30}{-10} \\ t=3 \end{gathered}[/tex]Hence, it takes 3 seconds for the ball to travel from the platform to the ground.
Finally we add the three times to determine the total time of the free fall; therefore the time the ball is free falling is 15 seconds.
b)
To determine the height of the platform we can use the fact that the time it takes the ball to fall from this height to the ground is six seconds, then using the second equation we have that:
[tex]\begin{gathered} y=0-60(3)+\frac{1}{2}(-10)(3)^2 \\ y=-225 \end{gathered}[/tex]This means that the ball travels 225 meters downward from the height of the platform to the ground, therefore the platform is 225 meters above the ground.
A long, thin wire offers more resistance to an electrical current than a thick, short wire would.TrueFalse
Answers
Resistance is directly proportional to the length of the conductor and inversely proportional to area of cross section.
Thus, the given statement is true.
tion 14A 37 kg child holds a 5.9 kg package in a 67 kg boat at rest, and then the child throws the packagehorizontally from the boat at a velocity of +12.4 m/s. What is the velocity of the boat after this?Vunits
Answers
Answer:
-0.704 m/s
Explanation:
The conservation of momentum demands that since the child + boat + box system is isolated, the initial momentum must equal the final momentum.
Now since initially, everything is at rest, the initial momentum of the system is zero.
The final momentum of the system is
[tex](m_c+m_b)v_1+(m_{\text{box}})v_2[/tex]where
m_c = mass of the child
m_b = mass of the boat
m_box mass of the boat
v1 = belcity of child + boat
v2 = veloctiy of the box.
Equating the initial momentum to the final momentum gives
[tex](m_c+m_b)v_1+(m_{\text{box}})v_2=0[/tex]Now in our case
m_c = 37 kg
m_b = 67 kg
v1 = unknown
m_box = 5.9 kg
v2 = 12.4
Therefore, the above equation gives
[tex](37+67)v_1+(5.9)(12.4)=0[/tex]solving for v1 gives
[tex]v_1=\frac{5.9\cdot12.4}{37+67}[/tex]which evaluates to give (rounded to the nearest hundredth)
[tex]\boxed{v_1=-0.70m/s}[/tex]which is our answer!
It takes less energy to cool a hot car than it does to cool a medium-sized home in Atlanta, Georgia during the summer!
false
true
Answers
The given statement is false.
Atlanta which is in Georgia have high temperatures during summer.
Although Georgia is near ocean but Atlanta is landlocked.
This place is also located a bit towards the tropic of cancer and this altitude is near to the equator.
With such a location, it is justified for the summers to be hot.
But in comparison to car, medium sized homes tend to cool down faster.
This is because of the good ventilation in the houses.
While in car, already the body is heat absorbing and traps heat in summer which then leads to the switching on of ACs in the car.
While in such hot summer when the AC is turned on then the ventilation becomes null. Which makes the hot air rise above and the cool air settle down.
But since there's no way for hot air to move, it remains inside the car and make it hotter in the summer and this in turn make people turn on their AC at cooler temperature and for longer time, thus consuming in more energy.
While in house, due to proper ventilation, there's a movement maintained in the atmosphere.
Therefore, it takes more energy to cool a hot car than it does to cool a medium-sized house in Atlanta during summer.
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Jennifer uses many forms of energy to get ready for school in the morning. Which table best matches each form of energy to Jennifer's actions?
Answers
Answer:
c I think
Explanation:
pretty sure cuz of common sense
Answer:
A form of energy you use when cheering for your favorite team. answer choices. sound energy. electrical energy. thermal energy. electromagnetic energy.
Explanation:
Hoped it helped :))))
A boat with initial position (5i -2j+ 4k) metres relative to port, acceleratesuniformly from initial velocity (4i+ j-3k) m s^-1, for 8 seconds until reaching finalvelocity (12i-7j+13k) m s^-1.a)Find the position of the object after 8 seconds.b) Find the acceleration of the object.
Answers
Given,
The initial position of the boat, d_i=(5i-2j+4k) m
The initial velocity of the boat, u=(4i+j-3k) m/s
The time period, t=8 s
The final velocity of the boat, v=(12i-7j+13k) m/s
To find:
a) The position of the object after 8 s
b) The acceleration of the object.
Explanation:
a)
From the equation of motion, the total distance traveled by the object is given by,
[tex]d=\frac{1}{2}(v+u)t[/tex]On substituting the known values,
[tex]\begin{gathered} d=\frac{1}{2}[(12\hat{i}-7\hat{j}+13\hat{k)}+(4\hat{i}+\hat{j}-3\hat{k})]8 \\ =4\times(16\hat{i}-6\hat{j}+10\hat{k}) \\ =(64\hat{i}-24\hat{j}+40\hat{k})\text{ m} \end{gathered}[/tex]Thus the final position of the boat is,
[tex]\begin{gathered} d_f=d_i+d \\ =\left(5\hat{i}-2\hat{j}+4\hat{k}\right)+(64\hat{i}-24\hat{j}+40\hat{k}) \\ =(69\hat{i}-26\hat{j}+44\hat{k})\text{ m} \end{gathered}[/tex]b)
The acceleration of an object is given by,
[tex]a=\frac{v-u}{t}[/tex]On substituting the known values,
[tex]\begin{gathered} a=\frac{(12\hat{i}-7\hat{j}+13\hat{k)}-(4\hat{i}+\hat{j}-3\hat{k})}{8} \\ =\frac{8\hat{i}-8\hat{j}+16\hat{k}}{8} \\ =(\hat{i}-\hat{j}+2\hat{k})\text{ m/s}^2 \end{gathered}[/tex]Final answer:
a) Thus the position of the boat after 8 s is
[tex]\begin{equation*} (69\hat{i}-26\hat{j}+44\hat{k})\text{ m} \end{equation*}[/tex]The acceleration of the boat is
[tex]\begin{equation*} (\hat{i}-\hat{j}+2\hat{k})\text{ m/s}^2 \end{equation*}[/tex]Assume the motion of Oscillator is defined
As y = 2 cos6πt - Sin5πt. If the mass of
Oscillator is 10 gram,
What are the Mascimum and
minimum kinectic energy.
Answers
Explanation:
B. Choose will (‘ll) or (be) going to, whichever is correct or more likely, and one of these verbs (7 marks- half each).
Get out of the building! It sounds like the generator isgoing toexplode.
Roman _____________ early before she reaches 65. She mentioned it at the meeting recently.
A: I think _____________ home across the park.
B: That’s a good idea.
Next year, no doubt, more people _____________ the competition as the prize money increases.
A: Can we meet at 10.00 outside the ILS building?
B: Okay. I_____________ you there.
Don’t sit on that bench, I_____________.
I’m not feeling well. In fact, I think I_____________.
‘Closed over the new year period. This office _____________ on 2nd January’ (a sign on an office window).
I’m sure you _____________ a good time staying with Merga.
We _____________ with Kedija tonight. She’s asked us to be there at 7:00.
‘The 2.35 to Arba Minch_____________ from gate 5’ (announcement at the airport).
I wouldn’t walk across the old bridge if I were you. It looks like it ____________.
I read in the paper that they _____________the price of the gas again.
Do you like my new solar watch? Here, I_____________you how it works.
A: AtoMessay isn’t in his office at the moment.
B: In that case, I_____________him at home.