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

`Time = 7.5\ seconds`

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

`(-4t)/(-4) = (0)/(-4)`

`t = (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

`(4t)/(4) = (30)/(4)`

`t = (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