Question

Nicole throws a ball straight up. Chad watches the ball from a window 5.0 m 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?

Short answer

The velocity at which the ball is thrown up is 14.14 m/s

Step-by-step solution

Write the information given 

The height of Chad is $h_1=5.0m$

While coming back to the ground, the speed of the ball as it passes Chad is $v_1=10m/s$
Let the maximum height reached by the ball is $H$

Let the initial velocity of the ball is $v_i$
The velocity of the ball at the maximum height is $v=0m/sec$

Let the final velocity of the ball is $v_f$

The acceleration due to gravity is$g=10m/s^2$

Step 2. To determine the initial velocity of the ball

Write the equation of motion,

$$\begin{gathered} {v_1}^2-{v_i}^2=2a{h}_1 \\ {v_i}^2={v_1}^2-2(-10)5 \\ {v_i}^2={10}^2+100 \\ {v}_i=\sqrt{200}=14.14m/s \end{gathered}$$
Therefore, the velocity at which the ball is thrown up is 14.14 m/s