Question

50 POINTS! A Boy throws a ball horizontally a distance of 22m downrange from the top of a tower that is 20.0m tall. What is his throwing velocity?

Answer 1

Answer: 11m/s.

Explanation: 11m/s.

Answer 2

The ball's horizontal and vertical velocities at time
`t` are

`v_x=v_(xi)`

`v_y=v_(yi)-gt`

but the ball is thrown horizontally, so
`v_(yi)=0`. Its horizontal and vertical positions at time
`t` are

`x=v_(xi)t`

`y=20.0\,\mathrm m-\frac g2t^2`

The ball travels 22 m horizontally from where it was thrown, so

`22\,\mathrm m=v_(xi)t`

from which we find the time it takes for the ball to land on the ground is

`t=(22\,\rm m)/(v_(xi))`

When it lands,
`y=0` and

`0=20.0\,\mathrm m-\frac{9.8(\rm m)/(\mathrm s^2)}2\left((22\,\rm m)/(v_(xi))\right)^2`

`\implies v_i=v_(xi)=11(\rm m)/(\rm s)`