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
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.
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