Math Problem Statement
A golfer stands 420420 ft (140140 yd) horizontally from the hole and 4040 ft above the hole (see figure.) Assuming the ball is hit with an initial velocity of 120120 ft/s, at what angle (or angles) should it be hit to land in the hole? Assume the path of the ball lies in a plane. use 32 for g
Solution
To solve this, we can break the motion of the ball into horizontal and vertical components, using the principles of projectile motion. We'll assume that the angle at which the ball is hit is .
Given dataTo solve this, we can break the motion of the ball into horizontal and vertical components, using the principles of projectile motion. We'll assume that the angle at which the ball is hit is .
Given
- Distance from golfer to hole horizontally:
- Distance from golfer to hole vertically: (since the golfer is above the hole)
- Initial velocity:
- Acc
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Math Problem Analysis
Mathematical Concepts
Projectile Motion
Trigonometry
Kinematics
Formulas
Horizontal distance: d_x = v_0 * cos(θ) * t
Vertical distance: d_y = v_0 * sin(θ) * t - 0.5 * g * t^2
Time of flight: t = (2 * v_0 * sin(θ)) / g
Theorems
Projectile Motion Equations
Suitable Grade Level
Grades 11-12
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