# Velocity at the midway point

## Homework Statement

The velocity at the midway point of a ball able to reach a height y when thrown with a velocity v0 at the origin is:

v2=v02+2ay

## The Attempt at a Solution

I made y = 1/2 y and the simplified the equation to v=sqrt(v02+ay)
But that is wrong because the answer is sqrt(v02/2)
Why?

TSny
Homework Helper
Gold Member
See if you can continue to simplify your result. In particular, can you find a way to express ay in terms of v0?

a = (v-v0)/t
y = v0t+1/2 at2
Substituting those don't seem to help enough

TSny
Homework Helper
Gold Member
In your first post, you stated the following useful equation: v2 = vo2 + 2ay.

In your problem, y represents the height to which the ball will reach (i.e., the maximum height). When the ball reaches maximum height, what can you say about the value of v on the left side of the equation?

• 17Blue
Oh wow, then you get ay = - v02/2
and then if you plug that back into my first equation, you get the answer.
Wouldn't have thought of that. Thanks!

• 17Blue
Can you please explain more ?