Question

A soccer ball bounces straight up into the air off the head of a player from a height of 6 feet. .......h(t) = -16t^2+40r+6, where h is the height of the ball at t seconds. How long does it take the ball to hit the ground

Answer 1

Explanation:

the ground = 0 ft.

so,

0 = -16t² + 40t + 6

let's simplify

0 = -8t² + 20t + 3

the general solution of a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -8

b = 20

c = 3

t = (-20 ± sqrt(400 - 4×-8×3))/(2×-8) =

= (-20 ± sqrt(400 + 96))/-16 =

= (-20 ± sqrt(496))/-16 = (-20 ± 4×sqrt(31))/-16

t1 = (-20 + 4×sqrt(31))/-16 = 20/16 - sqrt(31)/4 =

= 5/4 - sqrt(31)/4 = -0.141941091... s

t2 = (-20 - 4×sqrt(31))/-16 = 20/16 + sqrt(31)/4 =

= 5/4 + sqrt(31)/4 = 2.641941091... s

a negative time duration does not make sense for our scenario here, so t2 = 2.641941091... s is our solution here.

it takes the ball 2.641941091... seconds to hit the ground.