Question

A toy rocket lifts off at an initial velocity of 102 feet per second from a height of 10 feet. The height of the rocket can be modeled by the equation h = – 16t2 + 102t + 10, where ‘t' is the time in seconds. When will the rocket hit to the ground?

Answer 1

6.47secs

Explanation:

Given the height of the rocket modelled by the equation;

h = – 16t^2 + 102t + 10, where ‘t' is the time in seconds

The rocket will hit the ground at h = 0

Substitute into the equation

– 16t^2 + 102t + 10 = 0

Multiply through by -1

16t^2-102t-10 = 0

t = 102±√(102)²-4(16)(-10)/2(16)

t = 102±√10404+640/32

t = 102±√11044/32

t = 102 ±105.09/32

t = 102+105.09/32

t = 207.09/32

t = 6.47secs

Hence it will take 6.47secs for the rocket to hit the ground