Question

A sandbag is released from a hot air balloon that is 400ft above the ground. Using the falling object model, h = –16t2 + s, where h = height in feet, t = time in seconds, and s = initial height in feet, how long will it take for the sandbag to hit the ground?

A.
25 seconds
B.
4 seconds
C.
5 seconds
D.
20 seconds

Answer 1

It takes 5 seconds for the sandbag to hit the ground

Step-by-step explanation:

Given:

Height at which the sand bag is released from the hot air balloon
`= -400 f t`

To find:

Time taken for the sandbag to hit the ground, t =?

Solution:

The initial height =s

Initially the height will be 0

Hence
`s=0`

the falling object model equation

`h=-16 t^(2)+s`

Substituting the values we get,

`h=-16 t^(2)+s`

`400=16 t^(2)`

`t^(2)=(400)/(16)`

`t^(2)=25`

`t=√(25)`

`t=5 \text { seconds }`

Result:

Thus it takes 5 seconds for the sandbag to hit the ground