Question

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?

Answer 1

(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

$s=ut+\frac{1}{2}gt^2$

where

u = 0 is the initial velocity

t is the time

$g=9.8 m/s^2$ 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:

$t=\sqrt{\frac{2s}{g}}$

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

$t=\sqrt{\frac{2(5)}{9.8}}=1.01 s$

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

$t=\sqrt{\frac{2(10)}{9.8}}=1.43 s$

(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:

$v=u+gt$

where

v is the final velocity

u = 0 is the initial velocity

$g=9.8 m/s^2$ 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

$v=0+(9.8)(1.01)=9.9 m/s$

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

$v=0+(9.8)(1.43)=14.0 m/s$