A58.5-kg athlete leaps straight up into the air from a trampoline with an initial speed of 8.8 m/s. the goal of this problem is to find the maximum height she attains and her speed at half maximum height.

1) Maximum height
This is a uniformly accelerated motion with initial speed and acceleration (the negative sign is required because the acceleration is directed downward, in the opposite direction of the motion, which is directed upward). The distance covered (S) in a uniformly accelerated motion is related to the acceleration and the initial and final velocity by the relationship

At maximum height, S=h and the final velocity is zero: . So we can solve for h and find the maximum height:



2) Speed at half maximum height
Half maximum height corresponds to . To find the speed at this height, we can use the same relationship used in the previous step:

where is the speed at half maximum height.
Re-arranging and substituting numbers, we find

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