Question

A golf ball is struck at the base of a long hill that has a constant incline. The ball's trajectory (path) through the air is modeled by h = 0.0015d^2 + d, where h is the height of the ball above the tee and d is the horizontal distance from the tee. The height of the hill is modeled by h = 0.58d. Assuming the ball is struck at the point (0, 0), how far along the hill (horizontally!) does the ball land? (Round to the nearest foot.)

A) 130 feet
B) 129 feet
C) 131 feet
D) 132 feet

Answer 1

To find where the golf ball lands on the hill, we solve the equation 0.0015d^2 + d = 0.58d, which results in a horizontal distance of approximately 380 feet. However, this solution does not match any of the given answer choices, indicating a possible error in the question or the answer options.

Step-by-step explanation:

The student is asking for assistance in finding the distance along the hill where a golf ball lands after being struck from the tee. The golf ball's flight is described by the equation h = 0.0015d^2 + d, detailing its height above the tee in relation to the horizontal distance d from the tee. The hill's incline is modeled by the equation h = 0.58d.

To find the landing point, we need to set the two equations equal to each other since that is where the height of the ball and the height of the hill are the same.

Solving the equation 0.0015d^2 + d = 0.58d, we can rearrange to get 0.0015d^2 - 0.57d = 0. Factoring out d, we get d(0.0015d - 0.57) = 0. The non-zero solution to this equation gives us the horizontal distance where the golf ball lands on the hill.

Upon solving, we find that d ≈ 380 feet. However, since none of the options given (130, 129, 131, 132 feet) match this distance, there might be a constant misunderstanding or typo within the problem as it was provided. The student should verify the parameters of the problem or the potential answers with their instructor.