Question

The Lunar Roving Vehicle used in NASA’s late Apollo missions reached an unofficial lunar land speed of 5.0m/s by astronaut Eugene Cernan. If the rover was moving at this speed on a flat lunar surface and hit a small bump that projected it off the surface at an angle of 20°, how long would it be "airborne" on the Moon?

a) 0.86 s
b) 1.13 s
c) 1.42 s
d) 1.78 s

Answer 1

To determine the time the Lunar Roving Vehicle would be airborne on the moon after hitting a small bump, we can analyze the horizontal and vertical components of its motion. The vertical component of the initial velocity can be determined using the given angle, and then the time taken to reach maximum height can be calculated. Using these equations, we find that the rover would be airborne for approximately 1.07 seconds.

Step-by-step explanation:

To determine how long the Lunar Roving Vehicle would be airborne on the moon, we need to calculate the time it takes for the rover to reach its maximum height and then fall back to the surface. This can be done by analyzing the horizontal and vertical components of the motion.

First, let's find the vertical component of the initial velocity. We can use the given angle of 20° to find the vertical component:

Vertical component of initial velocity (vy) = initial velocity (v) * sin(angle)

Given that the initial velocity is 5.0 m/s and the angle is 20°, we can calculate:

vy = 5.0 m/s * sin(20°)

Using a calculator, we find vy ≈ 1.71 m/s.

Next, we can use the vertical component of velocity to find the time taken to reach maximum height (tup), assuming no air resistance:

tup = vy / g

Since the acceleration due to gravity on the moon is about 1/6 that of Earth (g=1.6 m/s²), we can calculate:

tup = 1.71 m/s / 1.6 m/s² ≈ 1.07 s.

Therefore, the rover would be airborne for approximately 1.07 seconds.