On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a golf club improvised from a tool. The free-fall acceleration on the moon is 1/6 of its value on earth. Suppose he hit the ball with a speed of 33m/s at an angle 28∘ above the horizontal.

To find the range and maximum height of the golf ball hit on the moon during the Apollo 14 mission, we can use the following equations of motion:

1. Vertical motion:
The initial vertical velocity (Vy) can be found using the given angle and initial speed:
Vy = V * sin(θ), where V is the initial speed and θ is the angle above the horizontal.

The time it takes for the ball to reach its maximum height can be found using the equation:
t_max = Vy / g, where g is the acceleration due to gravity on the moon (1/6 * 9.8 m/s^2).

The maximum height (H_max) can be found using the equation:
H_max = (Vy^2) / (2 * g).

2. Horizontal motion:
The time of flight (T) can be found using the equation:
T = (2 * Vy) / g.

The horizontal range (R) can be found using the equation:
R = V * cos(θ) * T.

Using these equations, we can calculate the values:

Given:
V = 33 m/s (initial speed)
θ = 28 degrees (angle above the horizontal)
g = 1/6 * 9.8 m/s^2 (acceleration due to gravity on the moon)

Calculations:
Vy = V * sin(θ)
t_max = Vy / g
H_max = (Vy^2) / (2 * g)
T = (2 * Vy) / g
R = V * cos(θ) * T

Once you substitute the values into the respective equations, you will be able to calculate the maximum height (H_max) and horizontal range (R) of the golf ball hit on the moon during the Apollo 14 mission.