A trapeze artist, starting from rest, swings downward on the bar, lets go at the bottom of the swing, and falls freely to the net. An assistant, standing on the same platform as the trapeze artist, jumps from rest straight downward. Friction and air resistance are negligible.

Question

A trapeze artist, starting from rest, swings downward on the bar, lets go at the bottom of the swing, and falls freely to the net. An assistant, standing on the same platform as the trapeze artist, jumps from rest straight downward. Friction and air resistance are negligible.

(a) On which person, if either, does gravity do the greatest amount of work?
*the person with more mass
*trapeze artist
*assistant

Explain

(b) Who, if either, strikes the net with a greater speed?
assistant
trapeze artist
neither

My solution
a) I say more work is done on the assistant because as he moves upwards he resists gravity, thus more work is required to overcome the resistance.

b) trapeze artist

(a) It is not clear from the workding of your question whether the platform is at the elevation where the trapeze artists begins or ends his swing. If they begin at the same elevation, gravity does more work on the more massive person. The trapeze does no work while it is held, because motion is perpedicular to the tension force in the trapeze ropes.
(b) neither The kinetic energy is propertional to mass, but mass gets divided out when computing velocity.
Not all of the trapeze artist's velocity will be vertical

So if I understand this , u meant the body with vertical displacement has more speed, which would be the assistant since he jumps (vertically) downward

No, that is not what I meant. They both have the same speed (and KE), but the trapeze artist has some of that speed directed horizontally due to the time he spent swinging forward on the trapeze.

So with that said it means the trapeze artist will land with a lesser speed because some of his speed is directed horizontally. Thanks

Answer 1

Yes, the trapeze artist will have a greater overall speed as they fall, but some of it will be directed horizontally due to their initial swing. However, in terms of vertical speed, both the trapeze artist and the assistant will be the same when they hit the net, since both are acted upon by the same gravitational force and started from rest.

Answer 2

Yes, that is correct. The trapeze artist will land with a lesser speed compared to the assistant because some of their speed is directed horizontally during the swing.

Answer 3

No, that is not correct. The trapeze artist will actually have a greater speed when they strike the net compared to the assistant. This is because the trapeze artist is able to build up more kinetic energy during their swing, which translates into a higher velocity when they let go and fall freely towards the net. In contrast, the assistant jumps straight downward without any initial velocity, so their speed is lower when they hit the net.