Platform diving in the olympic games takes place at two heights: 5 meters and 10 meters. what is the velocity of a diver entering the water from each platform if he steps off the platform initially? how much time does it take the diver to reach the water from each platform?

(a) Time of flight: 1.01 s and 1.43 s

The motion of a diver jumping from a platform and entering the water is a free-fall motion, so its vertical displacement is given by

where

u = 0 is the initial velocity

t is the time

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

If we re-arrange the equation, we can solve for t, the time it takes for each diver to enter the water:

For the diver jumping from 5 m, s = 5 m, so we get

For the diver jumping from 10 m, s = 10 m, so we get

(b) final velocity: 9.9 m/s and  14.0 m/s

In order to find the final velocity of each diver as they enter the water, we can now use the following suvat equation:

where

v is the final velocity

u = 0 is the initial velocity

is the acceleration of gravity

t is the time at which the diver enters the water

For the diver jumping from 5 m, t = 1.01 s, so the final velocity is

For the diver jumping from 10 m, t = 1.43 s, so the final velocity is