Question

A ball is launched upward from the ground with an initial velocity of 20 ft/s. The height of the ball at time t is represented by the function h(t). h(t)=-16t^2+20t, where t is measured in seconds and h(t) is measured in feet. drag the values to the lines to complete each sentence.

1. The ball reaches its maximum height when t is ____ seconds.

2. The maximum height of the ball is ____ feet.

3. The balls hits the ground when t is ____ seconds.


OPTIONS: 0.4 0.625 0.8 1.25 5.44 6.25 12.5 25

Answer 1

1.-t₁ = 0,625 s

2.-h(max) = 6,25 f

3.-t = 1,25 s

Explanation:

V₀ = 20 f/s

h(t) = - 16*t² + 20*t

h(max) = ??

h´(t) = - 32*t + 20

h(max) will occurs when V = 0 dh/dt = 0 then

- 32*t + 20 = 0

- 32*t = -20

t = 20/32

t₁ = 0,625 s

h(max) = h(0,625) = - 16*(0,625)² + 20*0,625

h(max) = - 6,25 + 12,5

h(max) = 6,25 f

c) The ball will hit the ground

t = 2*t₁

t = 2*0,625

t = 1,25 s