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.
To determine whether the ball will clear the tree, we need to consider the height of the tree and the maximum height the ball can reach.
Let's break down the problem step by step:
1. Draw a diagram: Draw a horizontal line to represent the ground. Mark a point to represent Sam, where the ball is hit, and another point to represent the tree, which is 35 m in front of Sam and 45 m tall. Label these points accordingly.
2. Determine the horizontal distance: The horizontal distance the ball travels is given as 120 m. Represent this on the diagram by drawing a horizontal line from Sam's starting point to a point 120 m away. You can label this line as the horizontal distance.
3. Determine the maximum height: The ball has a maximum height of 80 m. Draw a vertical line from the horizontal distance line to represent the maximum height.
4. Compare the height of the tree and the maximum height of the ball: In the diagram, compare the height of the tree (45 m) with the maximum height of the ball (80 m). You need to check whether the maximum height of the ball is higher than the height of the tree.
5. Analyze the result: If the maximum height of the ball is greater than the height of the tree, then the ball will clear the tree. Otherwise, if the maximum height is less than or equal to the height of the tree, the ball will hit the tree.
In this case, based on the information given, we can see that the maximum height of the ball (80 m) is greater than the height of the tree (45 m). Therefore, the ball will clear the tree and continue beyond it.