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

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 \(\theta\).

### 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 \(\theta\).

### Given 
- Distance from golfer to hole horizontally: \( d_x = 420 \, \text{ft} \)
- Distance from golfer to hole vertically: \( d_y = -40 \, \text{ft} \) (since the golfer is above the hole)
- Initial velocity: \( v_0 = 120 \, \text{ft/s} \)
- Acc

A golfer stands 420 ft (140 yd) horizontally from the hole and 40 ft above the hole. Assuming the ball is hit with an initial velocity of 120 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.

Discover how to calculate the angle(s) at which a golfer must hit a ball to land in a hole 420 ft away and 40 ft below, using projectile motion principles. This problem involves kinematics, trigonometry, and physics concepts, suitable for students in Grades 11-12.

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