During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched with an initial upward velocity of 78 ft/s. The height of the T-shirt (h) in feet after 𝑡 seconds is given by the function h = −16𝑡2 + 78𝑡 + 5. How long will it take the T-shirt to reach its maximum height? What is its maximum height?

Question

a. 1.22 s, 76.35 ft
b. 2.44 s, 146.28 ft
c. 2.44 s, 100.06 ft
d. 2.44 s, 131 ft

Answer 1

the time of max height (tmax) is on the axis of symmetry of the parabola

tmax = -b / 2a = -78 / (2 * -16) = 2.44 s

to find hmax , plug tmax into the height equation

Answer 2

The answer is C.

they didnt explain it very well. the formula of the problem is;
ax^2 + bx + c.

a = -16
b = 78
c = 2

the formula to find the variable “t” is;
-b/2a.

if you plug in the variables, it is;
-78/2( -16)
which in decimals is 2.4375 (or 2.44 for the answer)

now if you put the value of t in the equation it looks like;
-16(2.4375)^2 + 78(2.4375) + 5 = h

if you solve it, 100.0625 = h

The answers are t, h. If you round their values, you get 2.44s and 100.06ft.

Answer 3

Thanks @i+just+got+100 you are 100% correct and helpful!!!!!!!