Question

If a toy rocket is launched vertically upward from ground level with an initial velocity of 120 feet per second, then its height h after t seconds is given by the equation h(t) = -16t^2 + 120t. How long will it take the rocket to return to the ground? Group of answer choices

Answer 1

Answer:

$Time = 7.5\ seconds$

Step-by-step explanation:

Given

$Equation:\ h(t) = -16t^2 + 120t$

$Initial\ Velocity = 160ft/s$

Required:

Determine the time taken to return to the ground

From the equation given; height (h) is a function of time (t)

When the rocket returns to the ground level, h(t) = 0

Substitute 0 for h(t) in the given equation

$h(t) = -16t^2 + 120t$

becomes

$0 = -16t^2 + 120t$

Solve for t in the above equation

$-16t^2 + 120t = 0$

Factorize the above expression

$-4t(4t - 30) = 0$

Split the expression to 2

$-4t = 0\ or\ 4t - 30 = 0$

Solving the first expression

$-4t = 0$

Divide both sides by -4

$\frac{-4t}{-4} = \frac{0}{-4}$

$t = \frac{0}{-4}$

$t =0$

Solving the second expression

$4t - 30 = 0$

Add 30 to both sides

$4t - 30+30 = 0+30$

$4t = 30$

Divide both sides by 4

$\frac{4t}{4} = \frac{30}{4}$

$t = \frac{30}{4}$

$t = 7.5$

Hence, the values of t are:

$t =0$ and $t = 7.5$

$t =0$ shows the time before the launching the rocket

while

$t = 7.5$ shows the time after the rocket returns to the floor