A ball is hit horizontally at a height of 1.2 m and travels a horizontal distance of 5.0 m before reaching the ground. The ball is at rest when hit. Calculate the initial horizontal velocity given to the ball when it was hit.

In order to find the velocity, we need to know the distance covered by the ball in a known length of time. We are given the distance, 5.0 m, therefore we need to compute the time of flight of the ball. This will be the time taken by the ball to fall from the height of 1.2 m to the ground. Note that the initial velocity given to the ball is horizontal, this means that it has no vertical components and it does not affect the vertical fall of the ball. This simplifies the problem since we can find the time of flight simply calculating the time that it takes for a stationary object to fall from 1.2 m. We know the formula for the displacement y of a body experiencing constant acceleration: y= 1/2g(t^2) where g is the gravitational acceleration constant. We rearrange the equation and substitute the values of g and y= 1.2m to find t= 0.5s (note that we must quote our result with the same number of significant figures as the data given in the problem). Hence the ball traveled 5.0m in 0.5s, so we find the magnitude of the horizontal velocity, v= 10 m/s.