Severity of injuries during a vertical fall depends among other factors on the acceleration on the body suffers as it comes to rest.

In the example below we estimate the acceleration due to ground forces during a fall.

Let's assume that a ball is thrown off a ledge a height of 5m by launching upward with a velocity of 2.5 m/s hitting the ground with a velocity v.

To estimate the acceleration due to stopping from a vertical fall, let's break the motion into two parts.

Part 1:The time from the upward launch of the ball and the subsequent fall up to the point the ball is about to touch the ground with a velocity v. This is free fall motion.

(a) Calculate the velocity of the ball v as they reach the ground - just before touching the ground.

Draw a sketch for Part (1) indicating the positive and negative directions and the initial velocity. Show the useful description, the physics concepts, principles, or equations, all mathematical steps, and any cross-checks or making sense of the answer.

Part 2:The time that the ball hits the ground with velocity v and is acted upon by ground forces that decelerate the ball eventually stopping it. During this part ignore gravity.

(b) Assume that the ground is hard made of concrete and the ball come to rest in a time of 0.1s. Assuming constant acceleration, calculate the acceleration during the stopping phase.

Draw a sketch for Part (2) indicating the positive and negative directions and the initial velocity. Show the useful description, the physics concepts, principles, or equations, all mathematical steps, and any cross-checks or making sense of the answer.

(c) Compare the acceleration in Part 2 with gravity by taking the ratio of the two. Comment on the how big the acceleration is with respect to gravity.