Answers
The potential energy of gravity is given by:
[tex]\begin{gathered} E=mgh \\ where: \\ m=0.3 \\ h=2 \\ g=9.8 \\ so: \\ E=0.3\cdot2\cdot9.8 \\ E\approx5.9J \end{gathered}[/tex]Answer:
5.9 J
Related Questions
9. The graph is a plot of the velocity versus time for an objectmoving in a straight line. The x position of the objectat t = 0 seconds is 0 meters. At what time after t = 0 secondsdoes the object again pass through its initial position?(a) 1 second(b) Between 1 and 2 seconds(c) 2 seconds(d) 3 seconds
Answers
Velocity:
The velocity in simple word, is defined as the change in the position of the particle with respect to the time. The velocity is considered as a vector quantity as it has both the magnitude and direction in it. It can be measured or calculated in meter per second.
At t = 2 seconds, the speed of an object is -10 m/s. As it passes through its initial position. Hence the correct answer is (2)
A uniform 500 N/C electric field points in the positive y-direction and acts on an electron initially at rest. After the electron has moved4.00 cm in the field, what is the energy of electron in eV?
Answers
Given data:
* The electric field in the y-direction is,
[tex]E=500\text{ N/C}[/tex]* The distance traveled by the electron is,
[tex]\begin{gathered} d=4\text{ cm} \\ d=0.04\text{ m} \end{gathered}[/tex]Solution:
The work done in terms of electric field is,
[tex]W=\text{Edq}[/tex]where q is the charge on an electron,
Substituting the known values,
[tex]\begin{gathered} W=500\times0.04\times1.6\times10^{-19}\text{ J} \\ W=\frac{500\times0.04\times1.6\times10^{-19}}{1.6\times10^{-19}}\text{ eV} \\ W=500\times0.04\text{ eV} \\ W=20\text{ eV} \end{gathered}[/tex]This work done is stored in the charge in form of energy.
Thus, the energy of the electron in eV is 20 eV.
A block with a mass m1 is hit by a force of magnitude F which causes the block to have an acceleration of magnitude a. If a second block of mass m2 is hit by the same force of magnitude F which causes the block to have an acceleration of magnitude 2a, then which of these could be the two masses? A) m1= 200kg ; m2= 100kgB) m1= 50kg ; m2= 25 kgC) m1= 100kg ; m2= 50kgD)m1= 10kg ; m2= 50kgE)Any of these
Answers
We are given that a force "F" accelerates an object of mass "m1". According to Newton's second law, this can be represented by the following equation:
[tex]F=m_1a[/tex]Now, we are given that a second object of mass "m2" is accelerated by "2a" using the same force. Using Newton's second law we get:
[tex]F=m_2(2a)[/tex]Now, we will divide both equations, we get:
[tex]\frac{F}{F}=\frac{m_1a}{m_2(2a)}[/tex]Now, we simplify by canceling put the "F" and the "a":
[tex]1=\frac{m_1}{2m_2}[/tex]Now, we multiply both sides by "2m2", we get:
[tex]2m_2=m_1[/tex]Therefore, the first mass must be twice the second mass.
The options that meet this condition are:
[tex]m_1=200kg,m_2=100kg\text{ }[/tex][tex]m_1=50kg,m_2=25kg[/tex][tex]m_1=100kg,m_2=50kg[/tex]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
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
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
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.
The postal service will not ship goods over 50 lbs without a special label. Donovan wants to estimate the weight of his package so he doesn't exceed the weight limit. He has a cast iron skillet that weighs 5.67 lbs, a dictionary that weighs 8.34 lbs, and a set of dishes that weighs 37.88 lbs. What will the estimated weight of Donovan's package be if he rounds each item to the nearest pound before totaling the weight?
Answers
52 Lb
Explanation
Step 1
round each itme to the nearest pound.
in this case, Rounding a price to the nearest pound is the same as rounding a decimal to the closest whole number
so
for example, If the price is $3.80 you can round up to $4 because the number in the tenths position is 8. The closest whole number to 3.8 is 4
hence
[tex]\begin{gathered} cast\text{ iron=5.67 Lbs}\rightarrow6\text{ LB} \\ dictionary=8.34\text{ Lb}\rightarrow8\text{ Lb} \\ a\text{ set of disehes=}37.88\text{ Lb}\rightarrow38\text{ Lb} \end{gathered}[/tex]Step 2
now, add the cost of the items to find the weight of the package
[tex]\begin{gathered} Weight_{package}=Weight_{cast}+Weight_{dictironay}+Weight_{dishes}\text{ } \\ \text{replace} \\ Weight_{package}=6\text{ lb+8 lb +38 lb=52 lb} \end{gathered}[/tex]therefore, the answer is
52 Lb
I hope this helps you
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.
A 100-N ball suspended by a rope A is pulled to one side horizontally by another rope B and supported so that the rope A makes an angle of 30º with the vertical wall (see figure). Find the tensions of the ropes A and B. You solve it for me by fi uwu
Answers
Tension in A rope = 58.115 N
Tension in B rope = 116.23 N
What is tension?Tension is defined as the force transmitted through a rope, cord, or wire when pulled by forces acting from opposite sides. Tension is transmitted along the length of the wire, drawing energy evenly into the bodies at both ends. T = mg + ma
Where;
T = tension, (N)
m = mass (kg)
g = gravitational force, 9.8 m/s²
A = acceleration (m/s²)
As, F = mg
100 = m x 9.8
m = [tex]\frac{100}{9.8}[/tex]
m = 10.20 kg
Let the tension in A rope be T₁ and in the B rope be T₂ which is making angle of 30⁰
The vertical component of tension T₂ will balance the weight
= T₂ cos 30 = 10.20 x 9.8
T₂ = [tex]\frac{99.96}{cos 30}[/tex]
Since cos 30 = [tex]\frac{\sqrt{3} }{2}[/tex]
T₂ = [tex]\frac{99.96}{0.86}[/tex]
T₂ = 116.23 N
The horizontal component of T₂ will balance T₁
T₂ sin 30 = T₁
116.23 sin 30 = T₁
T₁ = 116.23 × [tex]\frac{1}{2}[/tex]
T₁ = 58.115 N
To know more about tension visit:
https://brainly.com/question/13309648
#SPJ4
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.
(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.
Homework: Action-reaction forces area. equal in magnitude and point in the same directionb. equal in magnitude and point in opposite directionsc. unequal in magnitude but point in the same directiond. unequal in magnitude and point in opposite directions
Answers
We will have that they are:
Equal in magnitude and point in opposite directions. {Option B]
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.
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.
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".
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.
Learn more about the new force:https://brainly.com/question/14276767
#SPJ1
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!
A newly invented ride called Crazy Box in an amusement park has a strong magnet. The magnet accelerates the boxcar and its riders from zero to 35 m/s in 5 seconds. Suppose the mass of the boxcar and riders is 6,000 kg. What is the acceleration of the boxcar and its riders? What is the average net force exerted on the boxcar and riders by the magnets?
Answers
Answer:
Below
Explanation:
Acceleration = change in velocity / change in time = 35/5 = 7 m/s^2
F = m * a
= 6000 kg * 7 m/s^2 = 42 000 N
The average net force exerted on the boxcar and its riders by the magnets is 42,000 N.
What is the average net force?The average net force exerted on the boxcar and riders by the magnets is calculated as;
F(net) = ma
where;
m is massa is accelerationThe acceleration is calculated as;
a = Δv / Δt
a = 35 m/s / 5 s
a = 7 m/s²
The acceleration of the boxcar and its riders is 7 m/s².
The average net force exerted on the boxcar and riders by the magnets is;
F = 6,000 kg x 7 m/s²
F = 42,000 N
Thus, the average net force exerted on them is determined as 42,000 N.
Learn more about net force here: https://brainly.com/question/14361879
#SPJ2
The wavelength of red helium-neon laser light in air is 632.8 nm.(a) What is its frequency?Hz(b) What is its wavelength in glass that has an index of refraction of 1.63?nm(c) What is its speed in the glass?Mm/sNeed Help?Read ItWatch ItSubmit Answer
Answers
ANSWER:
(a) 4.74*10^14 Hz
(b) 388.22 nm
(c) 184 Mm/s
STEP-BY-STEP EXPLANATION:
We have the following information:
[tex]\begin{gathered} \lambda=632.8\text{ nm} \\ n=1.63 \end{gathered}[/tex](a)
To calculate the frequency we use the following formula:
[tex]\begin{gathered} f=\frac{c}{\lambda} \\ c=3\cdot10^8\text{ m/s} \\ \lambda=632.8\text{ nm }=632.8\cdot10^{-9}\text{ m} \\ \text{replacing:} \\ f=\frac{3\cdot10^8}{632.8\cdot10^{-9}} \\ f=4.74\cdot10^{14}\text{ Hz} \end{gathered}[/tex](b)
In this case, we apply the following:
[tex]\begin{gathered} \lambda_1=\frac{\lambda}{n} \\ \text{ replacing} \\ \lambda_1=\frac{632.8}{1.63} \\ \lambda_1=388.22\text{ nm} \end{gathered}[/tex](c)
To calculate the speed it would be:
[tex]\begin{gathered} v=\frac{c}{n} \\ \text{ replacing} \\ v=\frac{3\cdot10^8}{1.63} \\ v=1.84\cdot10^8 \\ v=184\text{ Mm/s} \end{gathered}[/tex]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 person pushes on a hockey puck with their stick at an angle so the vertical force is 22 N[down] and the horizontal force is 45 N [forward]. Assume the ice is frictionless.a) What is the actual force the hockey player transmits to the puck?b) What is the work done by the person pushing the hockey stick if they push the puck for 3.0s as it moves with a constant velocity of 22 m/s [forward]?c) What is the significance of the fact that both the horizontal force and motion are bothforwards?
Answers
50.08 Newton is the actual force the hockey player transmits to the puck and 3305.93 Joule is the work done by the person pushing the hockey stick if they push for 3.0s as it moves with a constant velocity of 22 m/s
(a)
Given, horizontal force Fx = 45 N, vertical force Fy = 22 N
Thus, the total force acting on the is F = [(Fx)^2 + (Fy)2]^1/2
Therefore, F = [(45N)^2 + (22 N)2]^1/2 = 50.08 N
(b)
Constant velocity v = 22 m/s and time interval t = 3.0 s
The horizontal distance travelled by the is x = v t = (22 m/s) (3.0 s) = 66 m
The work done by the person pushing the hockey stick is W = F. x = (50.08 N) (66 m) = 3305.93 J
(c) The magnitude of the horizontal force is greater than (almost double) the vertical force, so the motion of is in the same direction as the horizontal force. The horizontal force dominates here.
To know more about force visit : https://brainly.com/question/13191643
#SPJ9
Please help me!A boy on a skateboard travels the first 600m of a trip at an average speed of 2 m/s. He then travels the next 800m in 200s and spends the last 100s at a speed of 5 m/s. Find the average speed of the bicyclist for this trip.
Answers
average speed = total distance / total time
speed x time = distance
part 1
D1= 600 m, s1=2m/s
Part 2
d2=800m, t2=200s
Part 3
s3=5m/s ,t3=100s
time1 = Distance1/speed1 = 600m/2m/s = 300s
Distance3 = speed3 x time 3 = 5 m/s x 100s = 500m
Total distance = d1+d2+d3 = 600 + 800 + 500 = 1900m
Total time = t1+t2+t3 =300 + 200 + 100 = 600 s
Avg speed = 1900m/600s = 3.17 m/s
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.
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.
To know more about summer, refer: https://brainly.com/question/11971528
#SPJ9
A farm tractor tows a 3300 kg trailer up a 14 degree incline with a steady speed of 2.8 m/s. What force does the tractor exert on the trailer?
Answers
We are asked to determine the force that the tractors is exerting on a trailer up an incline. A free-body diagram of the situation is the following:
Where:
[tex]\begin{gathered} F=\text{ force of the tractor} \\ m=\text{ mass of the trailer} \\ g=\text{ acceleratio of gravity} \end{gathered}[/tex]Now, we add the forces in the direction of the incline:
[tex]\Sigma F_x=F-mg_x[/tex]To determine the x-component of "mg" we use the following right triangle:
Now, we use the function sine to determine the value of "mgx":
[tex]\sin14=\frac{mg_x}{mg}[/tex]Now, we multiply both sides by "mg":
[tex]mg\sin14=mg_x[/tex]Now, we substitute the values of "m" and "g":
[tex](3300kg)(9.8\frac{m}{s^2})\sin14=mg_x[/tex]Solving the operations:
[tex]7823.75N=mg_x[/tex]Now, we substitute the value in the sum of forces:
[tex]\Sigma F_x=F-7823.75N[/tex]Since the object is moving at a steady speed this means that the sum of forces is zero:
[tex]F-7823.75N=0[/tex]Now, we add 7823.75N to both sides:
[tex]F=7823.75N[/tex]Therefore, the tractor exerts a force of 7823.75N
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.
Learn more about centripetal force here: https://brainly.com/question/20905151
#SPJ1
Answer:
C in the tension in the string
Explanation:
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.
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]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
Imagine an asteroid at rest in space that cracks into two pieces. The first piece moves at 1.4 times the speed of the second piece. Calculate the ratio of the first piece’s mass to the second piece’s mass
Answers
Since the total linear momentum of the system was 0 before the asteroid cracking into two pieces, then the magntude of the linear momentum of each piece must be the same after the cracking.
Then:
[tex]m_1v_1=m_2v_2[/tex]If the speed of the first piece is 1.4 times the speed of the second, then:
[tex]\begin{gathered} v_1=1.4v_2 \\ \Rightarrow m_1\times1.4v_2=m_2v_2 \\ \Rightarrow1.4m_1=m_2 \\ \Rightarrow m_1=\frac{m_2}{1.4} \\ \Rightarrow\frac{m_1}{m_2}=\frac{1}{1.4} \end{gathered}[/tex]Then, the ratio of the first piece's mass to the second piece's mass is 1:1.4