Velocity at the midway point

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1. Jan 3, 2015

rasen58

1. The problem statement, all variables and given/known data
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:

2. Relevant equations
v2=v02+2ay

3. 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?

2. Jan 3, 2015

TSny

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

3. Jan 4, 2015

rasen58

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

4. Jan 4, 2015

TSny

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?

5. Jan 4, 2015

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!

6. Nov 12, 2015

mohamed hamdy

Can you please explain more ?