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

Answer:

1.-t₁  =  0,625 s

2.-h(max)  =  6,25 f

3.-t = 1,25 s

Step-by-step 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