Question

A toy rocket blasts straight up off the gound with an initial velocity of 50 ft/s. How long will the rocket remain in the air? Use the formula h = -16t2 + 50t where h is the height of the rocket in feet and t is the time in seconds after liftoff. Assume no air resistance, and that the rocket has no propelling force after liftoff. Round your answer to the nearest tenth.

Answer 1

Given , h = -16$t^{2}$ + 50t where h is the height of the rocket in feet and t is the time in seconds after liftoff.

The rocket will remain in the air till it reaches the ground.

To find the time taken to reach the maximum height we use a formula

t = $\frac{-b}{2a}$

From the given equation , a= -16 , b= 50

Apply the values in the formula

t = $\frac{-50}{2(-16}$

t = 1.5625 seconds

The rocket will reach the maximum point in 1.5625 seconds and it reaches the ground in another 1.5625 seconds.

1.5625 + 1.5625 = 3.125 seconds

The rocket will remain in the air for 3.1 seconds