Question

An object is dropped from a platform 400 ft high. Ignoring wind resistance, how long will it take to reach the ground?

Answer 1

Let's convert the initial height from feet to meters first:

`h=400 ft=121.9 m`

The object is in free fall, so it is moving by uniformly accelerated motion with constant acceleration
`g=9.81 m/s^2` (gravitational acceleration) from initial height h=121.9 m. Its vertical position at time t is given by

`y(t)=h- (1)/(2)gt^2`

We want to know how long it will take to reach the ground, therefore we should calculate the time t at which the vertical position y(t) becomes zero:

`0=h- (1)/(2)gt^2`
rearranging,

`t= \sqrt{ (2h)/(g) }= \sqrt{ (2(121.9 m))/(9.81 m/s^2) }=4.98 s`