A kicked ball reaches h meters above the ground after t seconds using the formula: h= -5t^2+20t.?

Question

a) how long is the ball air born?
b) What is the maxium hieght the ball reaches?
c) When does it reach the maxium height?
d) give all steps to these questions.

Answer 1

a) Find out when it hits the ground, by setting the height equal to zero and solving for t:

0 = -5t² + 20t = -5t(t - 4)

t = 0 or t = 4, so it's airborne for 4 seconds.

b) The maximum height is reached at the halfway point (note: this only true when the initial position is zero...see part d). So plug in t = 2:

h(2) = -5(2)² + 20(2) = =-5(4) + 40 = -20 + 40 = 20 meters.

c) Again, it reaches the maximum height at the halfway point, t = 2.

d) Just to prove that the ball reaches its maximum height at t = 2, put the equation in parabola form:

h = -5(t² - 4t)
h = -5(t² - 4t + 4 - 4) = -5(t² - 4t + 4) + 20
h = -5(t - 2)² + 20

So the vertex is (2, 20), meaning that the maximum height is h = 20 meters at t = 2 seconds.