Question

If a toy rocket is launched vertically upward from ground level with an initial velocity of 148 ft per second then it’s hight h after t seconds is given by the equation h(t)=-16t^2+148t how long will it take the rocket to return to the ground

Answer 1

The rocket will take 9.25 seconds to return to ground

Solution:

Given that toy rocket is launched vertically upward from ground level with an initial velocity of 148 ft per second

Height "h" after "t" seconds is given by equation:

$h(t) = -16t^2 + 148t$

To find: time taken by rocket to return to ground

The time taken by rocket to return to ground is found by substituting h(t) = 0 in above equation

$0 = -16t^2 + 148t$

First take "t" as common term

$t(-16t + 148) = 0$

Zero product property. The zero product property states that if a⋅b = 0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5) = 0

So for above equation we get,

$t = 0 \text{ or } -16t + 148 = 0$

-16t + 148 = 0

-16t = -148

t = 9.25

When t = 0 , the rocket would not left the ground. So ignore t = 0

So t = 9.25

So the rocket will take 9.25 seconds to return to ground