Question

PLEASE HURRY!!!!

The height h in feet of an object shot straight up with initial velocity v in feet per second is given by h = −16t^2 + vt + c, where c is the initial height of the object above the ground. A model rocket is shot vertically up from a height of 6 feet above the ground with an initial velocity of 22 feet per second. Will it reach a height of 10 feet? Identify the correct explanation for your answer.



A. No; The discriminant is positive so the rocket will reach a height of 10 feet.

B.Yes; The discriminant is positive, so the rocket will reach a height of 10 feet.

C.No; The discriminant is negative, so the rocket will not reach a height of 10 feet.

D.Yes; The discriminant is zero, so the rocket will reach a height of 10 feet.

Answer 1

B.

Explanation:

We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:

10 = -16t^2 + 22t + 6

Rewriting the equation in standard quadratic form:

16t^2 - 22t + 4 = 0

Using the quadratic formula:

t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))

t = (22 ± sqrt(36))/32

t = 3/4 or 1/4

Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.