Question

The equation h(t)= -16t^2+864t models the path of a rocket shot into the air. After how many seconds does the rocket hit the ground?

Answer 1

t = 54 seconds

Explanation:

The equation that models the path of a rocket into the air is given by :

`h(t)= -16t^2+864t`

It is required to find the time after which the rocket will hit the ground. When it hits the ground, the height of the rocket will becomes zero. It means,

h(t) = 0

i.e.

`-16t^2+864t=0\\\\16t(-t+54)=0\\\\16t=0, -t+54=0\\\\t=0\ and\ t=54\ s`

It means after 54 seconds, the rocket will hit the ground.