Question

Juli is going to launch a model rocket in her backyard. When she launches the rocket, the function h(t)=−16t^2+32t models the height, h, of the rocket above the ground as a function of time, t. Find the zero of this function that tells us when the rocket will hit the ground after it is launched.

Answer 1

The zero function the rocket will hit the ground is

t2= 2s

Explanation:

`h(t)= -16 t^(2)+32t\\ h=0m\\0=-16 t^(2)+32t\\0=t(-16t+32)\\t1=0\\t2=-16t+32\\16t=32\\t=(32)/(16)=2s\\ t2=2`

Checking

t2=0

`h(t)=-16t^(2) +32t\\h(2)=-16*2^(2)+32*2\\h(2)=-16*4+32*2\\h(2)=-64+64=0\\h(2)=0 m`