Question

Sports A baseball is thrown into the air with an upward velocity of 30 ft/s. Its

height h, in feet, after t seconds is given by the function.h= -16t2 + 30t + 6. How
long will it take the ball to reach its maximum height? What is the ball's maximum
height? What is the range of the function?

Answer 1

Explanation:

so, the function is

h(t) = -16t² + 30t + 6

we get the point of the extreme value(s) by finding the zero solution(s) of the first derivative of the function.

h'(t) = -32t + 30

finding the zero solution

-32t + 30 = 0

30 = 32t

t = 30/32 = 15/16 seconds

after 15/16 seconds (not even a full second) the ball reaches its maximum height.

the height at that maximum is then h(15/16) :

-16(15/16)² + 30×15/16 + 6 = - 15²/16 + 450/16 + 6 =

= -225/16 + 450/16 + 96/16 = 225/16 + 96/16 = 321/16 =

= 20.0625 ft

and so, the range (the interval or set of all valid functional values) is

0 <= h(t) <= 20.0625

as naturally, on a normal surface and environment, the height of the ball cannot go below 0 (when it hits the ground, it's over).