E. O-27.7 m/s9. An object of mass 2 kg moving with a speedof 26 m/s to the right collides with an objectof mass 13 kg moving with a speed of 2 m/sto the left. If the collision is completely inelastic,calculate their speed after collision. (1 point)A. O-0.831 m/sB. O 1.733 m/sC. 06.089 m/sD. O5.39 m/sE. O 0.388 m/s10. An object of mass 16 kg moving with a speed
Answers
Given
Mass of an object, m=2 kg
Velocity of the object, u=26 m/s towards right
Mass of the other object, m'=13 kg
Speed of the object, u'=2 m/s towards left
To find
If the collision is completely inelastic,calculate their speed after collision.
Explanation
Since the collision is perfectly inelastic, so after collision both the body would combine together and move as one
Let the velocity after collision be v.
Considering the direction towards right as positive.
Thus,
By conservation of momentum
[tex]\begin{gathered} mu+m^{\prime}u^{\prime}=(m+m^{\prime})v \\ \Rightarrow2\times26-13\times2=(2+13)v \\ \Rightarrow v=1.733\text{ m/s} \end{gathered}[/tex]Conclusion
The velocity is B. 1.733 m/s
Related Questions
If you have a mass of 65kg and the earth has a mass of 6 x 10^24. You are 6.4 x 10^6m from the center of earth. What is the Force you feel from the earth? G (the universal gravity constant) is 6.67 x 10^-11.
Answers
According to Newton's Law of Universal Gravitation, the gravitational force F between two particles with masses M and m separated by a distance r is given by:
[tex]F=G\frac{Mm}{r^2}[/tex]To find the force that you feel from the Earth, replace the value of the gravitational constant G, as well as M=6*10^24kg, m=65kg and r=6.4*10^6m:
[tex]\begin{gathered} F=(6.67\times10^{-11}N\frac{m^2}{\operatorname{kg}^2})\times\frac{(6\times10^{24}\operatorname{kg})(65\operatorname{kg})}{(6.4\times10^6m)^2} \\ =635N \end{gathered}[/tex]Therefore, the magnitude of the force that you feel due to your gravitational interaction with the Earth is 635 N.
an7. Pressure is calculated by dividing force by theover which the force is exerted.Which state of matter will hold its shape without a container?QPressure is calculated by dividing force by the “what”over which the force is exerted?
Answers
The pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Then, the missing word is area.
What is the total motion of an object along a path? Questions Time Distance Motion Displacement
Answers
The total motion of an object along a path is total distance covered in the given time.
What is motion?The phenomenon of an item changing its position with respect to time is known as motion in physics. In mathematics, displacement, distance, velocity, and acceleration are used to explain motion.
Motion is total distance covered or the displacement covered in the given time.
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Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number).(2+4i)⋅(2+4i) =
Answers
You have the following expression;
[tex](2+4i)(2+4i)[/tex]to perform the previous operation, expand the previous factors as follow:
[tex]\begin{gathered} (2+4i)(2+4i)=(2)(2)+(2)(4i)+(4i)(2)+(4i)(4i) \\ =4+8i+8i+16i^2 \\ =4+16i+16i^2 \end{gathered}[/tex]take into account that i^2 = -1, then, you obtain:
[tex]4+16i+16(-1)=4+16i-16=16i-12[/tex]Hence, the result is 16i - 12
A quarterback back pedals 2.2 meters southward and then runs 6.8 meters northward. What is the magnitude and direction of the displacement?
Answers
ANSWER
[tex]4.6m\text{ Northward}[/tex]EXPLANATION
Displacement is the shortest distance between the final position and the initial position of a body.
Taking the southward direction to be the negative direction and the northward direction to be positive, to find the displacement, we have to add the distances traveled by the quarterback.
Therefore, we have:
[tex]\begin{gathered} D=-2.2+6.8 \\ D=4.6m \end{gathered}[/tex]Since the displacement is positive, its direction is Northward.
Hence, his displacement is 4.6 m Northward.
Hello could you please help me with this question? is parallel to the y-axis and has an x-intercept of 3
Answers
Answer:
[tex]x=3[/tex]Explanation: We need to find the equation of a line that is parallel to the y-axis and has an x-intercept of 3:
This simply implies that the slope is infinite, and so the equation must be:
[tex]x=3[/tex]The plot of the equation:
NOTE! The plot matches the description of the problem.
Consider a 0.9 kg object traveling in a circle of radius 6 meters. The object completes 1 circles in 2 seconds traveling at constant speed. What net force is required to sustain this motion? [Hint: 2 is almost equal to 10.]
Answers
Mass of the object, m= 0.9 kg and radius of the circular path, r = 6 m and time, T = 2 seconds.
Here, the velocity will be
[tex]\begin{gathered} v=\frac{dis\tan ce}{time} \\ =\frac{2\pi r}{T} \end{gathered}[/tex]The force required to sustain this motion is
[tex]F=\frac{mv^2}{r}[/tex]Substituting the value of velocity, we get
[tex]\begin{gathered} F=\frac{m(2\pi r)^2}{rT^2} \\ =\frac{4m\pi^2r}{T^2} \\ =\frac{4\times0.9\times10\times6}{2^2} \\ =54\text{ N} \end{gathered}[/tex]
If a ball is dropped from a bridge that is 36.4 meters high, how long will it take until the ball hits the ground below the bridge?
Answers
2.72 sec
Explanation
Step 1
to solve this we need to use the formula
[tex]h=v_0t+\frac{1}{2}gt^2[/tex]let
[tex]\begin{gathered} v_0=0 \\ h=36.4\text{ m} \\ g=9.8\text{ }\frac{\text{m}}{s^2} \\ t=\text{ unknown= t} \end{gathered}[/tex]replace
[tex]\begin{gathered} h=v_0t+\frac{1}{2}gt^2 \\ 36.4=0\cdot t+\frac{1}{2}(9.8\text{ }\frac{m}{s^2})t^2 \\ 36.4=+(4.9\frac{m}{s^2})t^2 \\ \text{divide both sides by 4.9} \\ \frac{36.4}{4.9}=t^2 \\ t=\sqrt[]{7.42} \\ t=2.72 \end{gathered}[/tex]therefore, the answer is
2.72 sec
I hope this helps you
Which object is the greatest inertia A. 1500kg elephant B. 5kg rock moving at 300 m/sC. 100 kg football player moving at 5 m/sD. 1000 kg car moving at 40 m/s
Answers
Answer:
A. 1500 kg elephant
Explanation:
The inertia only depends on the mass and not on the velocity, so the greater the mass, the greater the inertia. It means that the object with the greaterst inertia is:
A. 1500 kg elephant
Because it has more mass.
Find the following for path C in the figure below (a) the total distance traveledm(b) the distance from start to finishm(c) the displacement from start to finishm
Answers
(a). The total distance traveled in the path C is,
[tex]\begin{gathered} D=\text{ From 2 m to 10 m + from 10 m to 8 m + from 8 m to 10 m} \\ =\mleft(10-2\mright)+\mleft(10-8\mright)+\mleft(10-8\mright) \\ =8+2+2 \\ =12\text{ m} \end{gathered}[/tex]Thus, the total distance traveled in the path C is 12 m.
(b). The distance from the start (2 m) to the finish (10 m) is,
[tex]\begin{gathered} d=\text{from 2 m to 10 m} \\ d=10-2 \\ d=8\text{ m} \end{gathered}[/tex]Thus, the distance traveled from start to finish is 8 m.
(c). The displacement from the start (2 m) to the finish (10 m) by neglecting the return travel in the path C is,
[tex]\begin{gathered} d^{\prime}=10-2 \\ d^{\prime}=8\text{ m} \end{gathered}[/tex]Thus, the displacement for the path C is 8 m.
QUESTION 3 Jessica and Julie are twins, with a mass of 40.0 kg each. They are both riding a merry go round, with Jessica sitting 8.0 m from the center and Julie sitting 6.0 m from the center. If Jessica is traveling at 1.3 m/s and Julie is traveling at 0.95 m/s, who is experiencing the greatest force?
Answers
Question 1001 10The device shown demonstrates which energy transformation?A Blectrical energy - electromagnetic energyB. Besteomaretic energy - Kinetic energyC. Yinetic energy-electrical energyD. Chemical energy-electromagnetic energyPlease answer this question!!
Answers
ANSWER
A. electrical energy → electromagnetic energy
EXPLANATION
The device shown is a lamp. To turn on the lamp we have to connect it to the electric power; there we have electrical energy. The lamp has a light bulb, which when it's on it emits light. Remember that light is an electromagnetic wave. Therefore the electrical energy is transformed into electromagnetic energy.
You deposit $2000 in an account earning 8% interest compounded monthly. How much will you have in the account in 5 years?
Answers
The amount in my account after 5 years, if a deposit $2000 will be $2985.62.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Tocalculate the amount, that will be in my account in 5 years, we use the formula below.
Fromula:
A = P(1+R/100n)ⁿˣ............... Equation 1Where:
A = AmountP = PrincipalR = Ratex = Timen = Total number of months in a yearFrom the question,
Given:
P = $2000R = 8%n = 12 monthsx = 5 yearsSubstitute these values into equation 1
A = 2000[1+8/(12×100)]⁵*¹²A = 2000(1+0.0067)⁶⁰A = 2000(1.0067)⁶⁰A = $2985.62Hence, the amount in my account will be $2985.62.
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Question 1 of 10Which is an alpha particle?O A. A particle with an atomic number of 2 and an atomic mass of 4O B. A particle with an atomic number of 4 and an atomic mass of 2O C. A particle with an atomic number of 2 and an atomic mass of 3D. A particle with an atomic number of 1 and an atomic mass of 3SUBMIT
Answers
Answer:
Explanation:
An alpha particle is a helium atom. It has a mass number of 4 and an atomic number of 2. Thus, the correct option is
E. O-8.237 kg m/s4. An object of mass 0.2 kg falling vertically downwardhits the ground with a speed of 13 m/s and bouncesback vertically upward with a speed 4 m/s. If the object was incontact with the ground for 0.5 seconds, calculate theaverage force exerted by the ground on the object. (1 point)A. 06.8 NB. 10.563 NC. 09.048 ND. 12.856 NE. 03.149 N5. An object was acted upon by a force of 24 for 0.8seconds. Calculate the change in its momentum. (1 point)
Answers
4)
We woud apply the formula for calculating rate of change of momentum which is expressed as
F = m(v2 - v1)/t
where
F is the force
m is the mass of the object
v2 is the final velocity
v1 is the initial velocity
t is the time
From the information given,
m = 0.2
v1 = -13
v2 = 4
t = 0.5
F = 0.2(4 - -13)/0.5
F = 6.8 N
5. Object A has a mass of 3 kg and is moving at 6 m/s before the collision with the 2 kg object B which is moving at -5 m/s. After the collision, object A has a velocity of 2 m/s. a. What is the total initial momentum of object A and B?b. What is the final velocity of object B after the collision?
Answers
Given,
The mass of object A is
[tex]m_1=3kg[/tex]The mass of object B is
[tex]m_2=2kg[/tex]The velocity of the object A before the collision is
[tex]u_1=6\text{ m/s}[/tex]The velocity of the object B before the collision is
[tex]u_2=-5\text{ m/s}[/tex]The velocity of object A after the collision is
[tex]v_1=2\text{ m/s}[/tex]Let the velocity of object B after the collision is v.
(a) The total initial momentum of objects A and B.
[tex]\begin{gathered} m_1u_1+m_2u_2=(3kg)\times(6\text{ m/s)+(2 }kg)\times(-5\text{ m/s)} \\ =18-10 \\ =8 \end{gathered}[/tex]The total initial momentum of objects A and B is 8.
(b) From the conservation of momentum,
[tex]\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ 8=(3kg)\times(2\text{ m/s)+(2 }kg)\times v \\ 2v=8-6 \\ v=1\text{ m/s} \end{gathered}[/tex]The final velocity of object B after the collision is 1 m/s.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
Answers
Answer:
it’s the last one chemical covered to mechanical
Explanation:
asked my science teacher to make sure it’s correct
A 25 kg mass is thrown from the ground to a height of 50 m. (a) find the kineticenergy of the mass at this height.; (b) find the potential energy of the mass at thisheight. ; (C) find the velocity of the mass when it reach the ground.
Answers
Given
m: mass
m = 25 kg
h: height
h = 50 m
Procedure
(a) Kinetic energy is directly proportional to the mass of the object and to the square of its velocity. At this height initial velocity is equal to zero
K = 0 J
(b) The potential energy of any given object is a measurement of its potential to do work, create heat and generate power.
[tex]\begin{gathered} U=mgh \\ U=25\operatorname{kg}\cdot9.8m/s^2\cdot50m \\ U=12250\text{ J} \end{gathered}[/tex](c) When the mass reaches the ground all the potential energy is transformed into kinetic energy.
[tex]\begin{gathered} \frac{1}{2}mv^2=U \\ \frac{1}{2}mv^2=12250J \\ v=\sqrt[]{\frac{2\cdot12250}{25\operatorname{kg}}} \\ v=31.30\text{ m/s} \end{gathered}[/tex]why is scientific notation used ?a. to round numbers to the nearest whole numberb. to promote reproducibility of datac. to increase the validity of datad. to express very large or very small numbers
Answers
Scientific notation is used to represent very large or very small numbers in a simple way.
Therefore, the answer is option D.
Please help with the following question.Mass of cylinder = m0
Answers
Given:
Mass of block = m0
Mass of cylinder = m0
Given that a cylinder is placed at the top of an incline and the block is also placed at the top of a separate rough incline.
Given that both objects reach the bottom of their respective inclines with the same translational speed, let's explain why.
Since the mass of the cylinder and mass of the block are the same, both objects can be said to be rolling down their respective inclines downward along the smooth slope due to the acceleration due to gravity.
In this case the downward acceleration of the cylinder will be higher than that of the block. Although the acceleration of the block should be higher due to the rotational inertia. This happens because the block is exposed to a higher frictional level(due to its rough incline) which causes it to slow down, hence its acceleration will now be apparently the same with that of the cylinder.
In this case, we now have equal initial velocities, equal masses, and equal acceleration.
Since these units are the same, both the block and the cylinder will have reach the bottom of their inclines with the same translational speed.
We have the figure below:
The current through a motor is 210 A. If a battery keeps a 12.0 V potential difference across the motor, what electric energy is delivered to the motor in 10.0 s?
Answers
Given:
the current through motor is
[tex]I=210\text{ A}[/tex]The potential of the battery is
[tex]V=12\text{ V}[/tex]The time is
[tex]t=10\text{ s}[/tex]Required: the energy delivered to the motor in 10 sec is?
Explanation:
first, we calculate the power delivered to the motor.
The power is given by
[tex]P=VI[/tex]Plugging all the values in the above relation, we get:
[tex]\begin{gathered} P=12\text{ V}\times210\text{ A} \\ P=2520\text{ watt} \end{gathered}[/tex]The energy delivered to the motor is given by
[tex]E=Pt[/tex]Plugging all the values in the above relation, we get:
[tex]\begin{gathered} E=2520\text{ w}\times10\text{ s} \\ E=25200\text{ J} \\ \end{gathered}[/tex]Thus, the energy delivered to the motor is 25200 J.
Explain in terms of IMF and KE why liquids assume the shape of any container into which they are poured, whereas solids are rigid and retain their shapes.
Answers
According to the Kinetic Molecular Theory, the kinetic energy of the particles of a solid is low enough as for the intermolecular forces to be enough to keep the atoms of a substance roughly at the same place from each other. On the other hand, the kinetic energy of the particles of a liquid is high enough as to overcome the intermolecular forces but not as high as to free the particles completely. Then, the molecules of a liquid can move away from each other, and they assume the shape of a container into which they are poured provided that there is a gravitational force pulling the particles of the liquid toward one side of the container.
To summarize:
The kinetic energy of the particles of a liquid is enough to allow them to move with respect to each other, whereas the kinetic energy of the particles of a solid is not enough to overcome the intermolecular forces, so they remain at the same place with respect to each other.
In an elastic collision, bumper cars 1 and 2 are moving in the same direction when bumper car 1 rear-end bumper car 2. The initial speed of car 1 is 7.73 m/s and car 2 is 4.01 m/s. The mass of car 2 is 57% greater than that of car 1.
(a) what is the final velocity in m/s of bumper car 1?
(b) what is the final velocity in m/s of bumper car 2?
Answers
a ) The final velocity after an elastic collision of bumper car 1 = 9.01 m / s
b ) The final velocity after an elastic collision of bumper car 2 = 1.73 m / s
According to law of conservation of momentum
m1 u1 + m2 u2 = m1 v1 + m2 v2
u1 = 7.73 m / s
u2 = 4.01 m / s
m2 = 0.57 m1
7.73 m1 + ( 4.01 * 0.57 * m1 ) = m1 v1 + 0.57 m1 v2
7.73 + 2.29 = v1 + 0.57 v2
v1 = 10.02 - 0.57 v2
According to law of conservation of energy
1 / 2 m1 u1² + 1 / 2 m2 u2² = 1 / 2 m1 v1² + 1 / 2 m2 v2²
7.73² m1 + ( 4.01² * 0.57 * m1 ) = m1 v1² + ( 0.57 * m1 * v2² )
59.75 + 9.17 = ( 10.02 - 0.57 v2 )² + 0.57 v2²
68.92 = 100.4 + 0.33 v2² - 11.42 v2² + 0.57v2²
10.52 v2² = 31.48
v2² = 2.99
v2 = 1.73 m / s
v1 = 10.02 - ( 0.57 * 1.72 )
v1 = 10.02 - 0.99
v1 = 9.01 m / s
Therefore,
a ) The final velocity after an elastic collision of bumper car 1 = 9.01 m / s
b ) The final velocity after an elastic collision of bumper car 2 = 1.73 m / s
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An iron railroad railis 750 ft long when the temperature is 34°C. What is its length (in ft) when the temperature is -18°C? (Round your answer to at least 3 decimal placeFt
Answers
Answer: Final length = 749.998 ft
Explanation:
We would assume that the coefficient of linear expansion of iron is 36 x 10^- 6/C
We would apply the formula for calculating linear thermal expansion which is expressed as
L1 = aL(θ2 - θ1)
where
L1 = change in length
L = original length
a = coefficient of linear expansion of iron
θ2 = final temperature
θ1 = initial temperature
From the information given,
L = 750
θ2 = - 18
θ1 = 34
a = 12 x 10^- 6/C
By substituting these values into the formula,
L1 = 36 x 10^- 6(- 18 - 34)
L1 = 36 x 10^- 6(- 52)
L1 = - 0.001872
Thus,
Final length - initial length = - 0.001872
Final length - 750 = - 0.001872
Final length = - 0.001872 + 750
Final length = 749.998 ft
2. Kevin is a member of the school's track and field team. His favorite event is throwing the shotput. In his last competition, Kevin exerted 165 N of force on the shot put, which accelerated28.5 m/s2. What was the mass of the shot put?
Answers
Given data
*Kevin exerted a force is F = 165 N
*The given acceleration is
[tex]a=28.5m/s^2[/tex]The formula for the mass of the shot put is given as
[tex]m=\frac{F}{a}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} m=\frac{165}{28.5} \\ =5.78\text{ kg} \end{gathered}[/tex]Thus, the mass of the shot put is m = 5.78 kg
(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 3.9% of their strength? %(b) How many percent would the current need to be increased to return the torque to original values? %
Answers
a) The torque of a DC motor is directly proportional to the flux of the magnetic field, thus, when we reduce the flux (strength of permanent magnet) by 3.9%, we also reduce the torque by 3.9%
b) The torque of the DC motor can also be written as T=k*phi*I, where I is the current on the static part of the assembly. Thus, in order to maintain this relation, if the new phi is 0.961 times the old phi, the new current will need to be 1/0.961 times the old current, and thus 4% higher
The volume of gas v held at a constant temperature in a closed container varies inversely with it's pressure P. If the V of gas is 1600 cm^3 when the P is 250 mm Hg, find the v when the P is 400 mm Hg?
Answers
Explanation
The volume of gas v held at a constant temperature in a closed container varies inversely with it's pressure P,in math terms it is
[tex]\begin{gathered} V\propto\frac{1}{P} \\ where\text{ V is the volume} \\ P\text{ is the presion} \end{gathered}[/tex]When Pressure is constant, Volume is directly proportional to temperature.
Step 1
given the data, we need to apply the formula for a constant temperature ,
[tex]\begin{gathered} V_2=\frac{P_1V_1T_2}{T_1P_2} \\ as\text{ the temperature is constatn} \\ V_2=\frac{P_1V_1}{P_2} \end{gathered}[/tex]so
[tex]\begin{gathered} V_2=\frac{250\text{ mmHg*1600 cm}}{400} \\ V_2=1000\text{ cm}^3 \end{gathered}[/tex]so, the answer is
[tex]1000\text{ cm}^3[/tex]I hope this helps you
Two boats start together and race across a 42-km-wide lake and back. Boat A goes across at 42 km/h and returns at 42 km/h. Boat B goes across at 21 km/h, and its crew, realizing how far behind it is getting, returns at 63 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins.(a) Which boat wins?o Boat Ao Boat Bo It's a tie(b) By how much?_____ km(c) What is the average velocity of the winning boat?_____ km/h
Answers
ANSWER
[tex]\begin{gathered} (a)\text{ Boat A} \\ \\ (b)\text{ }42\text{ km} \\ \\ (c)\text{ }0\text{ km/h} \end{gathered}[/tex]EXPLANATION
(a) To determine which boat wins, we have to find the total time the journey takes for each boat.
To do that, apply the formula for speed:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ t=\frac{d}{s} \end{gathered}[/tex]where d = distance traveled
t = time taken
For boat A, the time taken to go across and return is:
[tex]\begin{gathered} t=\frac{42}{42}+\frac{42}{42}=1+1 \\ \\ t=2\text{ hrs} \end{gathered}[/tex]For boat B, the time taken to go across and return is:
[tex]\begin{gathered} t=\frac{42}{21}+\frac{42}{63}=2+0.667 \\ \\ t=2.667\text{ hrs} \end{gathered}[/tex]We see that it takes boat B longer to complete the race. Hence, boat A will win the race.
(b) To determine how much boat A will win, we can look at the distances both boats cover. Notice that while getting across the lake, boat A travels twice as fast as boat B and travels at the same speed while returning.
This implies that in the time that boat A travels both laps of the race, boat B is just reaching the other end of the lake.
In other words, in the time that boat A travels 84 km, boat B travels 42 km.
Hence, boat A will beat boat B by a distance of:
[tex]\begin{gathered} 84-42\text{ km} \\ \\ 42\text{ km} \end{gathered}[/tex](c) In the race, the winning boat starts from one end of the lake, gets to the other end, and then, returns to the starting point.
This implies that the displacement of the boat is 0 km.
Velocity is given by dividing displacement by the time taken. Since the displacement is 0 km, the velocity of the winning boat, Boat A is 0 km/h
A 0.45 kg spike is hammered into a railroad tie. The initial speed of the spike is equal to1.9 m/s.If the tie and spike together absorb 22 per- cent of the spike’s initial kinetic energy as internal energy, calculate the increase in in- ternal energy of the tie and spike.Answer in units of J.
Answers
Given:
mass of the spike is
[tex]0.45\text{ kg}[/tex]initial speed od the spike is
[tex]v_=\text{ 1.9 m/s}[/tex]if the tie and spike together absorb 22 percent of the spike's initial kinetic energy.
Required:
calculate the increase in internal energy of the tie and spike.
Explanation:
here we apply conservation of energy.
[tex]\Delta U+\Delta K+\Delta P=0[/tex]total change in energy is zero.
here potential energy is not given so neglect that part. we have only
[tex]\Delta U+\Delta K=0[/tex][tex]\Delta U=-\Delta K[/tex]Here,
[tex]\Delta U=-(K_2-K_1)[/tex]K1 is initial kinetic energy and K2 is final kinetic energy that is equal to zero.
now we have
[tex]\Delta U=K_1[/tex]we know that kinetic energy is
[tex]K=\frac{1}{2}mv^2[/tex]then
[tex]\Delta U=\frac{1}{2}mv^2[/tex]plugging all the values in the above relation. we get
[tex]\begin{gathered} \Delta U=\frac{1}{2}\times0.45\text{ kg }\times(1.9\text{ m/s})^2\times0.22 \\ \Delta U=0.18\text{ J} \end{gathered}[/tex]Thus, the change in internal energy is
[tex]0.18\text{ J}[/tex]A ball is thrown upward with a speed of 38.0 m/s from the top of a building 240 m tall.a) How long will it take for this ball to reach the ground?b) How long will it take for this ball to reach the highest point?
Answers
A) The total time it takes for the ball to reach the ground = 11.702 seconds
B) The time taken by the ball to reach the highest point = 3.8 seconds
Explanations:To get the distance from the top of the building to the maximum height reached by the ball:
[tex]v^2=u^2\text{ + 2gh}[/tex]The initial speed, u = 38 m/s
The final speed at the maximum height, v = 0m/s
g = -10m/s² (Since the ball is thrown upwards)
[tex]\begin{gathered} 0^2=38^2+2(-10)h \\ 20h\text{ = }1444 \\ h\text{ = }\frac{1444}{20} \\ h\text{ = }72.2\text{ m} \end{gathered}[/tex]The distance from the top of the building to the maximum height = 72.2 m
The time taken for the ball to reach the highest point from the top of the building will be calculated using the equation:
v = u + gt
0 = 38 + (-10)t
10t = 38
t = 38/10
t = 3.8 s
From the maximum height of the ball to the ground:
The height, H = 72.2 + 240
H = 312.2 m
The initial velocity, u = 0 m/s
g = 10 m/s²
Using the equation below:
[tex]\begin{gathered} v^2=u^2+2gH \\ v^2=0^2\text{ + 2(10)}(312.2) \\ v^2\text{ = }6244 \\ v\text{ = }\sqrt[]{6244} \\ v\text{ = }79.02\text{ m/s} \end{gathered}[/tex]The time spent from the top of the building to the the ground will be calculated using the formula:
v = u + gt
79.02 = 0 + 10t
10t = 79.02
t = 79.02/10
t = 7.902 s
The total time it takes for the ball to reach the ground = 7.902 + 3.8
The total time it takes for the ball to reach the ground = 11.702 seconds
The time taken by the ball to reach the highest point = 3.8 seconds