Question

A boy tosses a 0.5kg ball straight up into the air. How high updoes the ball go if the ball leaves the boy's hand with a speed of 5m/s? How much work does the boy do to the ball?

Answer 1

A boy tosses a 0.5 kg ball straight up into the air.

How high up does the ball go if the ball leaves the boy's hand with a speed of 5 m/s?

Recall from the equations of motion

$y=v_0t+\frac{1}{2}gt^2$

Where y is the maximum height achieved by the ball, v₀ is the initial velocity and t is the time.

Let us first find the time (t)

$v=v_0-gt$

Re-arranging the equation for time (t)

$t=\frac{v_0-v}{g}$

Where v is the final velocity of the ball and is zero at the maximum height and g is the gravitational acceleration.

$t=\frac{v_0-v}{g}=\frac{5-0}{9.8}=0.51\: s$

Now we can find the maximum height of the ball

$\begin{gathered} y=5\cdot0.51+\frac{1}{2}\cdot9.8\cdot(0.51)^2 \\ y=2.55+\frac{1}{2}\cdot2.55 \\ y=3.83\: m \end{gathered}$

Therefore, the maximum height of the ball 3.83 m