The height of a projectile launched upward at a speed of 32 feet/ second from a height of 128 feet is given by the function h(t)=-16t^2+32t+128. How long will it take the projectile to hit the ground?

8.51 seconds

Step-by-step explanation:

Time to reach maximum height

=( Usin90)/2g

= 32/2*9.81

= 32/19.62

= 1.63 s

Max height = U²Sin²tita/g

= 32²/9.81

= 1024/9.81

= 104.38ft

Total height=104.38 + 128= 232.38

Time to fall back to the ground using the formula

h = ut+(1/2)gt²

U= 0

H= 232.38

g = 9.81

(232.38 *2 )/9.81= t²

47.376= t²

t = 6.88 s

Total time taken to hit ground

= 6.88 + 1.63

= 8.51 seconds

6 meters

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."