Use the following scenario for the next three problems. A diver of mass m jumps
ID: 1438788 • Letter: U
Question
Use the following scenario for the next three problems.
A diver of mass m jumps into the air from a diving board at position A with an initial speed v0 and enters water at position B as shown. The diving board is a height H above the water. Neglect air resistance and possible rotational motion of the diver
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17. What is the kinetic energy of the diver just before he reaches the water at position B?
A)1/2 mv02
B) 2mgH
C)mgH + 1/2 mv02
D) mgH
E) Not enough information is given.
18. If the initial speed of the diver was 2v0 and everything else is the same, by how much does the work done by the earth on him as he moves from position A to position B increase?
A) 0
B) 2mgH
C) Sqrt 2mgH
D) mgH
E) Not enough information is given.
19. As the diver moves from position A to position B, what is the total change in gravitational potential energy of the system where the system contains only the diver?
A)The diver-earth system cannot store any gravitational potential energy.
B) ?mgH
C)mgH
D)2mgH
E)Not enough information is given.
Diving board WaterExplanation / Answer
17) As we know that, total energy of the system is the sum of its kinetic energy and its potential energy.
If diver move with velocity Vo then kinetic energy is,
K.E. = (1/2)m Vo2
And Potential energy is mgH. Where H is the height
So total energy is,
= mgH + (1/2)m Vo2
18) Te given condition is ,
initial speed of the diver was 2V0 and everything else is the same.
As we know work energy theorem,
Workdone is,
W = Kf - Ki
Kf = Final kinetic energy
Ki = Initial kinetic energy
If speed is same, both terms of kinetic energy is same.
Their substraction is Zero
So answer is Zero
19) The diver-earth system cannot store any gravitational potential energy because when diver reaches to the poin B, H = 0. So P.E. = 0 and diver-earth system cannot store any gravitational potential energy