Question

The quadratic equation h = - 1672 +32+ + 2 represents the helght, h (in feet), of a ball kicked aftert seconds. Answer each question

How long will it take the ball to reach 18 feet?
a. Approximately 2.68 seconds
b. Approximately 1.54 seconds
c. Approximately 3.12 seconds
d. Approximately 0.95 seconds

When will the object be at 10 feet?
a. Approximately 1.84 seconds
b. Approximately 2.25 seconds
c. Approximately 3.78 seconds
d. Approximately 0.67 seconds

When will the ball hit the ground?
a. Approximately 5.43 seconds
b. Approximately 4.29 seconds
c. Approximately 6.75 seconds
d. Approximately 3.92 seconds

Answer 1

The ball will take approximately 21.85 seconds to reach 18 feet.

Step-by-step explanation:

To find the time it takes for the ball to reach 18 feet, we can use the given quadratic equation h = -1672 + 32t + 2t^2. We set h to 18 and solve the equation.

18 = -1672 + 32t + 2t^2
2t^2 + 32t - 1672 + 18 = 0
2t^2 + 32t - 1654 = 0

This is a quadratic equation, so we can use the quadratic formula t = (-b ± sqrt(b^2 - 4ac)) / (2a) to solve for t. In this case, a = 2, b = 32, and c = -1654.

t = (-32 ± sqrt(32^2 - 4(2)(-1654))) / (2(2))
t = (-32 ± sqrt(1024 + 13232)) / 4
t = (-32 ± sqrt(14256)) / 4
t = (-32 ± 119.41) / 4

Since time cannot be negative, we take the positive value:
t ≈ (-32 + 119.41) / 4 = 87.41 / 4 ≈ 21.85 seconds