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## Homework Statement

A ball is thrown upward in such a way that its speed is 32.3 m/s when it is at half its maximum height. Find

(a) its maximum height,

(b) its velocity 2.0 s after it's thrown,

(c) its height 2.0 s after it's thrown, and

(d) its acceleration at its maximum height.

## Homework Equations

Constant acceleration equations:

v = v

_{0}+ at

x - x

_{0}= v

_{0}t + 1/2 (at

^{2})

v

^{2}= v

_{0}

^{2}+ 2a(x - x

_{0})

x - x

_{0}= 1/2 (v

_{0}+ v)t

x - x

_{0}= vt - 1/2 (at

^{2})

where v= velocity, a = acceleration, t = time, v

_{0}= initial velocity and x

_{0}= initial position

## The Attempt at a Solution

For (a), I thought the acceleration should be constant, since it is a free fall problem. At the ball's maximum height, v should equal 0. So I said:

0 = 32.3 m/s - (9.8 m/s

^{2})(t seconds)

t = 3.30 seconds, which should be the time it takes the ball to go from the halfway point to its maximum height, assuming subbing in speed for velocity didn't make the equation explode. I'm having trouble getting anything else useful without knowing the initial velocity or some other piece of information.