When you jump upward, your hang time is the time your feet are off the ground. Does hang time depend on the vertical component of velocity when you jump, the horizontal component of velocity, or both? 1. Both components 2. The horizontal component of your lift-off velocity 3. The vertical component of your lift-off velocity 4. Unable to determine

It only depends on the vertical component

Explanation:

Hello!

The horizontal component will tell you how much you travel in that direction.

You could have a large horizontal velocity, but if the vertical velocity is zero, you will never be out of the ground. Similarly, you could have a zero horizontal velocity, but if you have a non-zero vertical velocity you will be some time off the ground. This time can be calculated by two means, one is using the equation of motion (position as a function of time) and the other using the velocity as a fucntion of time.

For the former you must find the time when the position is zero.

Lets consider the origin of teh coordinate system at your feet

y (t) = vt - (1/2) gt^2

We are looking for a time t' for which y (t') = 0

0 = vt' - (1/2) gt'^2

vt' = (1/2) gt'^2

The trivial solution is when t'=0 which is the initial position, however we are looking for t'≠0, therefore we can divide teh last equation by t'

v = (1/2) gt'

Solving for t'

t' = (2v/g)