Question

30 point question! WILL AWARD BRAINLIEST!

A ball is thrown across a playing field from a height of h = 5 ft above the ground at an angle of 45° to the horizontal at the speed of 20 ft/s. It can be deduced from physical principles that the path of the ball is modeled by the function
y = − (32/(20^2))x2 + x + 5


Find the horizontal distance the ball has traveled when it hits the ground. (Round your answer to one decimal place.)

Answer 1

y = [-32/(20)^2]x^2 + x + 5
a.) For maximum height, y' = 0
y'= (-32/200)x + 1 = 0
32/200x = 1
x = 200/32 = 6.25
The maximum height attained by the ball is [-32/(20)^2](6.25)^2 + 6.25 + 5 = 8.125 feet.

b.) At the point the ball hits the ground, y = 0
y = [-32/(20)^2]x^2 + x + 5 = 0
x = 16.3 ft