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+(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=(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=(v_0-v)/(g)=(5-0)/(9.8)=0.51\: s`

Now we can find the maximum height of the ball

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

Therefore, the maximum height of the ball 3.83 m