Velocity at the midway point

[rasen58]

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:

Homework Equations

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]

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

 

[rasen58]

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

 

[TSny]

In your first post, you stated the following useful equation: v² = v_o² + 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?

 

[rasen58]

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!

 

[mohamed hamdy]

Can you please explain more ?