Question

During a soccer game, a goalie kicks a ball upward from the ground. The equation h(t)=−16t2+42t
represents the height of the ball above the ground in feet as a function of time in seconds. When the ball begins moving downward toward the ground, a player from the other team intercepts the ball with his chest 5 feet above the ground. How long after the goalie kicks the ball does the player intercept the ball?

 

(1 point)
Responses

1516
 seconds
1 and 5 over 16 seconds

5
 seconds
5 seconds

18
 seconds
1 eighth seconds

212
 seconds
2 and 1 half seconds

258
 seconds

Answer 1

Choose from the answers below

1 and 5 over 16 seconds


5 seconds


1 eighth seconds


2 and 1 half seconds

2 and 5 eight seconds
 

Answer 2

The player intercepts the ball when h(t) = 5.

Therefore, -16t^2 + 42t = 5

-16t^2 + 42t - 5 = 0

Using the quadratic formula, t = (-42 ± √(42^2 - 4*(-16)*(-5)))/(2*-16)

t = (-42 ± √(1764 - 320))/(-32)

t = (-42 ± √1444)/(-32)

t = (-42 ± 38)/(-32)

t = -1 or t = 5/4

Since time cannot be negative, the player intercepts the ball 5/4 seconds or 1 and 1/4 seconds after the goalie kicks the ball.

Therefore, the answer is 1 and 1/4 seconds.

Answer 3

The actual answer is 1 and 5 over 16 seconds. Apologies for the oversight. Thank you for providing the answer choices.