a golfer needs to hit a ball a distance of 500 feet, but there is a 60-foot tall tree that is 100 feet in front of the point whe

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a golfer needs to hit a ball a distance of 500 feet, but there is a 60-foot tall tree that is 100 feet in front of the point whe

re the shot needs to land. given that the maximum height of the shot is 120 feet, and that the intended distance of 500 feet is reached, by how much did the ball clear the tree?

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-03-17T03:55:01+03:00

We can formulate the trajectory of the parabola using the vertex form equation: y = a (x – h)^2 + k. The coordinates for the vertex are at h and k, representing the peak height, thus h = 250 and k = 120. Consequently, the equation becomes y = a (x – 250)^2 + 120. At the starting point where x = 0 and y = 0, we find a: 0 = a (0 – 250)^2 + 120, which simplifies to 0 = a (62,500) + 120, leading to a = -0.00192. The complete equation is y = -0.00192 (x – 250)^2 + 120. To determine y when x = 400, we substitute: y = -0.00192 (400 - 250)^2 + 120, yielding y = 76.8 ft. Hence, the ball clears the tree by 76.8 ft – 60 ft = 16.8 ft.