What is the initial velocity of the ball thrown by Nicole?

[ae4jm]

[SOLVED] How fast was the ball thrown?

Homework Statement

Nicole throws a ball straight up. Chad watches the ball from a window 5.0m above the point where Nicole released it. The ball passes Chad on the way up, and it has a speed of 10 m/s as it passes him on the way back down. How fast did Nicole throw the ball?

Homework Equations

Vf=Vi + at
y=Vi(t)+.5a(t)(^2)
Vf^2=Vi^2+2(a)(y)

The Attempt at a Solution

I've tried starting with the final V =0 and I've tried to solve the downward motion of the ball first, to attempt to get maybe the y value, or height of the ball at it's max. Please, where should I start? What am I missing?

 

[mgb_phys]

A hint, since no energy is lost - the speed going back down at a point is the same as the speed going up at that same height.
You just need v^2 = u^2 + 2as be careful of the signs!

 

[ae4jm]

Thanks mgb_phys! I finally got the correct answer of initial velocity=14 m/s.

for v^2 = u^2 + 2as; I let the -10 m/s of the downward velocity, u, = + 10 m/s at the same height of 5m on the upward velocity. I let v = unknown variable and the acceleration was equal to -9.8 m/s^2, and s=5m for the height. Thanks for the explanation!