Question

The function h(t)=−16t2+7t+63 represents the height of a t-shirt launched from a t-shirt cannon after t seconds. a. Write an equation that tells us when the t-shirt hits the ground. b. At what time does the t-shirt hit the ground. SHOW ALL WORK. Round to 2 decimal places.

Answer 1

`(a)\ -16t^2 + 7t + 63=0`

`(b)\ t = 2.215`

Explanation:

Given

`h(t) = -16t^2 + 7t + 63`

Solving (a): Equation when it hits the ground.

This means that
`h(t) = 0`

So, we have:

`h(t) = -16t^2 + 7t + 63`

`-16t^2 + 7t + 63=0`

Solving (b): The value of t in (a)

`-16t^2 + 7t + 63=0`

Using quadratic formula, we have:

`t = (-b \± √(b^2 - 4ac))/(2a)`

This gives:

`t = (-7 \± √(7^2 - 4*-16*63))/(2*-16)`

`t = (-7 \± √(49+ 4032))/(2*-16)`

`t = (-7 \± √(4081))/(-32)`

`t = (-7 \± 63.88)/(-32)`

Split

`t = (-7 + 63.88)/(-32); or\ t = (-7 - 63.88)/(-32)`

`t = (56.88)/(-32); or\ t = (-70.88)/(-32)`

`t = -1.7775; or\ t = 2.215`

Time can't be negative; So:

`t = 2.215`