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 25 m/s at an angle 24 ∘ above the horizontal.
How long was the ball in flight?
How far did it travel?
Ignoring air resistance, how much farther would it travel on the moon than on earth?
See Related Questions: Tue, 4-29-14, 1:34 PM.
To find the time of flight, distance traveled, and the difference in distance between the moon and Earth, we can use the equations of projectile motion.
1. Time of Flight:
The time of flight can be calculated using the formula:
time = 2 * (initial vertical velocity) / (acceleration due to gravity on the moon)
On the moon, the acceleration due to gravity is 1/6 of its value on Earth. Therefore, the initial vertical velocity is (25 m/s) * sin(24°) and the acceleration due to gravity is (9.8 m/s^2) / 6.
2. Distance Traveled:
The horizontal distance traveled can be found using the formula:
distance = (initial horizontal velocity) * time of flight
The initial horizontal velocity is (25 m/s) * cos(24°).
3. Difference in Distance on Moon vs. Earth:
To find the difference in distance traveled on the moon compared to Earth, we can calculate the ratio of the acceleration due to gravity on the moon to Earth's gravity and multiply it by the distance traveled on Earth.
Here's how you can calculate these values:
Step 1: Calculate the time of flight
time = 2 * (25 m/s * sin(24°)) / ((9.8 m/s^2) / 6)
Step 2: Calculate the distance traveled
distance = (25 m/s * cos(24°)) * time
Step 3: Calculate the difference in distance on the moon vs. Earth
distance_diff = distance * (1/6) * (9.8 m/s^2)
By using these formulas and the given values, you can find the time of flight, distance traveled, and the difference in distance between the moon and Earth.