Question

A person standing at the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it horizontal velocity `v_i`. What must be its minimum initial speed if the ball is never to hit the rock after it is kicked?

Answer 1

Step 1: compute time t needed for the ball to fall under gravity at acceleration g from a height R.
Step 2: compute the initial horizontal velocity vi using the time computed in step 1 and the fact that the ball must travel distance R.

Explanation:

The person and the ball are positioned a height R above the ground. The ball must be kicked a total distance R in order to not hit the rock. Gravity will be acting on the ball. You should first calculate the time it will take for the ball to fall from a height R under gravitational acceleration g. Next, use this time to compute how much speed the ball will need to be given to travel a distance of R before impacting the ground.

Useful equations:
For step 1: `h=1/2 g t^2` ;h height, g acceleration, t time
For step 2: `d=vt` ;d distance, v velocity, t time