Aball is kicked from the top of a building with a velocity of 50 m/s and lands 165 m away from the base of the buildi
c) what is the vertical velocity of the ball when it hits the ground?

32.3 m/s

Explanation:

The ball follows a projectile motion, where:

- The horizontal motion is a uniform motion at costant speed

- The vertical motion is a free fall motion (constant acceleration)

We start by analyzing the horizontal motion. The ball travels horizontally at constant speed of

and it covers a distance of

d = 165 m

So, the total time of flight of the ball is

In order to find the vertical velocity of the ball, we have now to analyze its vertical motion.

The vertical motion is a free-fall motion, so the ball is falling at constant acceleration; therefore we can use the following suvat equation:

where

is the vertical velocity at time t

is the initial vertical velocity

is the acceleration  of gravity (taking downward as positive direction)

Substituting t = 3.3 s (the time of flight), we find the final vertical velocity of the ball: