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Question

The first word spoken on the surface of the Moon after Apollo 15 landed on July 30, 1971, was “Bam!” this was James Irwin’s involuntary reaction to their rather bone-jarring touchdown. “We hit harder than any other flights!” says Irwin. “And I was startled, obviously, when I said, ‘Bam!’” The reason for the “firm” touchdown of Apollo 15 was that the rocket engine was shit off when the lander was still 1.31 m above the lunar surface and moving downward with a speed of 0.152 m/s. From that point on the lander descended in a lunar free fall, with an acceleration of 1.62 m/s2. As a result, the landing speed of Apollo 15 was by far the largest of any of the Apollo missions. To visualize the descent of Apollo 15, consider its position-time curve during the final stages of landing, shown below. 

a. How much time did it take for the lander to drop the final 1.31 m to the Moon”s surface? 

b. What was the impact speed of the lander when it touched down? 

Answer 1

This is a problem where you use the equations of motion to solve for what you are asked for. You need to know 3/5 variables v₀, v, a, d, t.

a) (picking downward as positive) , you know v₀ = .152 m/s, a = g_moon = 1.62 m/s² and d = 1.31 m

The equation to solve for time is quadratic in t: d = v₀t + 1/2 at² (Plug in values and use Quadratic Formula.)

b) In order to find v, use 2ad = v² - v₀² and solve directly for v if you do this first in order to avoid the quadratic formula for t . If you already have the answer to (a), you can always solve for v using v = v₀ + at (The easiest equation to use).

Good luck!