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 θ\theta.

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 θ\theta.

Given

  • Distance from golfer to hole horizontally: dx=420ftd_x = 420 \, \text{ft}
  • Distance from golfer to hole vertically: dy=40ftd_y = -40 \, \text{ft} (since the golfer is above the hole)
  • Initial velocity: v0=120ft/sv_0 = 120 \, \text{ft/s}
  • 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