Question

An object is dropped from a height of 100 meters. The function below models the relationship between t , the number of seconds after the object is dropped, and f(t) , the height of the object after it is dropped. f(t)=100−4.9t^2 Approximately how many seconds does it take for the object to hit the ground?

Answer 1

`t = 4.52`

Explanation:

Given

`f(t) = 100-4.9t^2`

Required

Time it hits the ground

When the object hits the ground, the height is 0.

In other words:

f(t) = 0

So, we have:

`0= 100-4.9t^2`

Collect like terms

`4.9t^2 = 100`

Divide through by 4.9

`t^2 = (100)/(4.9)`

`t^2 = 20.4081632653`

Take positive square roots of both sides

`t = √(20.4081632653)`

`t = 4.51753951453`

`t = 4.52`

Hence, the ball hits the ground after 4.52 seconds