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

Answer:

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

$(b)\ t = 2.215$

Step-by-step 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:

$t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

This gives:

$t = \frac{-7 \± \sqrt{7^2 - 4*-16*63}}{2*-16}$

$t = \frac{-7 \± \sqrt{49+ 4032}}{2*-16}$

$t = \frac{-7 \± \sqrt{4081}}{-32}$

$t = \frac{-7 \± 63.88}{-32}$

Split

$t = \frac{-7 + 63.88}{-32}; or\ t = \frac{-7 - 63.88}{-32}$

$t = \frac{56.88}{-32}; or\ t = \frac{-70.88}{-32}$

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

Time can't be negative; So:

$t = 2.215$