Sam hits a golf ball with a five-iron a distance of 120 m horizontally. A tree 45 m high and 35 m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has maximum height of 80 m?
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Yes.
At the midpoint of the trajectory, 60 m from the point the ball is struck, the height of the ball is 80 m.
A point 35 m from Sam is 25 m from the midpoint. For an inverted parabola, distance below the midpoint height varies with the square of the horizontal distance from the midpoint.
The ball height at that point is
80 - (25/60)^2*80 = 80[1 - (5/12)^2]
= 66.1 m
The tree wil be cleared.
A point 35 m from Sam is 25 m from the midpoint. For an inverted parabola, distance below the midpoint height varies with the square of the horizontal distance from the midpoint.
The ball height at that point is
80 - (25/60)^2*80 = 80[1 - (5/12)^2]
= 66.1 m
The tree wil be cleared.
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