Question

Gabe drops a hammer from an apartment that is 30 meters above the ground. The height of the hammer in meters,h, after t seconds is modeled by the function below h(t)=-t^2-t 30 find the number of seconds it will take for the hammer to hit the ground

Answer 1

The hammer will hit the ground after 5 seconds.

Explanation:

The height of hammer is defined by the function

`h(t)=-t^2-t+30`

Where, t is time in seconds.

`h(t)=-t^2-6t+5t+30`

`h(t)=-t(t+6)+5(t+6)`

`h(t)=(t+6)(5-t)`

The value of h(t) is 0, when hammer will hit the ground.

`0=(t+6)(5-t)`

Equate each factor equal to 0.

`t=-6`

`t=5`

The time can not be negative, therefore hammer will hit the ground after 5 seconds.