Henry throws a tennis ball over his house. The ball is 6 feet above the ground when he lets it go. The quadratic function that models the height, in feet, of the ball after (t) seconds is p(t)=-16^2+46t+6. How long does it take for the ball to hit the ground?
A- 2 second
B- 3 seconds
C-4.5 seconds
D- 6 seconds
Answers
Answer:
Option C: It takes 3 seconds for the ball to hit the ground.
Explanation:
The given quadratic function is h=-16 t^{2}+46 t+6h=−16t
2
+46t+6 where h is the height in feet and t is the time in seconds.
We need to determine at what time the ball will hit the ground.
Time taken:
The time can be determined by substituting h = 0 in the function h=-16 t^{2}+46 t+6h=−16t
2
+46t+6
Thus, we get;
0=-16 t^{2}+46 t+60=−16t
2
+46t+6
Let us solve the quadratic expression using the quadratic formula.
Thus, we have;
t=\frac{-46 \pm \sqrt{46^{2}-4(-16) 6}}{2(-16)}t=
2(−16)
−46±
46
2
−4(−16)6
Solving, we get,
t=\frac{-46 \pm \sqrt{2116+384}}{-32}t=
−32
−46±
2116+384
t=\frac{-46 \pm \sqrt{2500}}{-32}t=
−32
−46±
2500
t=\frac{-46 \pm 50}{-32}t=
−32
−46±50
Thus, the values of t are given by
t=\frac{-46 + 50}{-32}t=
−32
−46+50
and t=\frac{-46 - 50}{-32}t=
−32
−46−50
t=\frac{4}{-32}t=
−32
4
and t=\frac{-96}{-32}t=
−32
−96
t=-\frac{1}{8}t=−
8
1
and t=3t=3
Since, t cannot take negative values.
Thus, the value of t is t=3t=3
Hence, the time taken by the ball to hit the ground is 3 seconds.
Therefore, Option C is the correct
Answer:
Option C: It takes 3 seconds for the ball to hit the ground.
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