- #1

Jimmy87

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## Homework Statement

Long answer question. Simon is a long jumper. He tries to run as fast as he can before he jumps. This enables him to jump much further than if he did without running.

Question: Use ideas about forces and motion to explain how running helps Simon jump further

## Homework Equations

KE = 1/2mv^2

GPE = mgh

P = mv

## The Attempt at a Solution

The forces acting during the run are static friction on the track's surface. As the runner pushes on the track the frictional force exerts an equal and opposite force on the runner. If this force is bigger than the resistive force, the runner will accelerate. This will cause the kinetic energy to increase.

The distance of the jump depends on the time the jumper is in the air and the forward speed during this time in the air. The time in the air is determined by the vertical velocity which is determined by the size of the vertically downward reaction force form the floor before he jumps. So if he pushes vertically down on the floor before he jumps he will have a vertical velocity and the larger this force is the larger the velocity. A larger vertical velocity gives a greater vertical kinetic energy which means there is a larger gravitational potential energy which means a greater distance (height) which means a longer time in the air. Is it ok to say that if you have more vertical KE then you are in the air longer because the opposing gravitational force is constant so if you have more kinetic energy you will take longer to stop (work = force x distance) before you come back down to the ground?

What I'm confused about is I found a similar question to this and the answer said the following:

"The distance of the jump is linked to the time in the air which is why the running is important beforehand"

I am confused with this as I would have thought that the time in the air is not at all related to running beforehand as they are on different planes (i.e.horizontal and vertical) which I thought were independent of each other. I would have thought that if you had no run up at all then the time in the air would be the same you just would have minimal horizontal velocity so you wouldn't jump very far. Also, one other question I had:

Does the run up help at all with the size of the vertical reaction force the runner is able to exert before the jump?