Question

During the half time of a basketball game, a sling shot launches T-shirts at the crowd. The T-shirt is launched with an initial upward velocity of 60 ft/s from a height of 5 feet.
Use f(x) = -12x^2 + 60x + 5 to help you answer the following questions,

a. How long will it take for the T-shirt to reach maximum height?

b. What is the maximum height ?

Answer 1

Step-by-step explanation:

The T-shirt is launched with an initial upward velocity of 60 ft/s from a height of 5 feet. Its equation of motion is given by :

$f(x) = -12x^2 + 60x + 5$ ....(1)

(a) For maximum height, put $\dfrac{df(x)}{dt}=0$

So,

$\dfrac{ d(-12x^2 + 60x + 5)}{dt}=-24x+60$

Now put,

$-24x+60=0\\\\x=2.5\ s$

So, the time taken for the T-shirt to reach maximum height is 2.5 seconds.

(b) Put x = 2.5 s in equation (1)

$f(x=2.5) = -12(2.5)^2 + 60(2.5) + 5\\\\f(x)=80\ \text{feet}$