Physics Motion Problem!!! Please help!!!?

Actually you can solve this purely on the information given - assuming you only need to know the vertical component of the velocity.

Use the equation v² = u² + 2as

This is a constant acceleration problem, where v is the final velocity, u is the initial velocity and a is the acceleration.

We know the following:-

The acceleration in the vertical direction is due to gravity, -9.8 m/s².

The initial velocity u is what we are trying to find. For the minimum initial velocity to result in hitting the roof, the final velocity v, must be zero when the ball reaches a vertical height (s) of 86 metres. You can then put these values in the equation:-

0 = u² + 2 * -9.8 * 86

u² = √1685.6

Hence u = 41.06 m/s.

NOTE - this is the vertical component of velocity only. There will be a horizontal component also, unless he is directly under the roof apex and striking the ball vertically upward.

To find the horizontal component, you need the distance he is away from the apex, or at least the angle the ball leaves the bat. The vertical component will always be the value above.

Once you know both horizontal and vertical components, you can use Pythagoras to find the resultant, overall initial velocity.

We need to know the distance from the building unless he is standing beside it and hitting the ball vertically up!