Question

The first word spoken on the surface of the Moon after Apollo 15 landed on July 30 1971 was "Bam". The reason for this was that the rocket engine was shut off a bit early when the lander was still 4.3ft above the lunar surface and moving downward with a speed of 0.5ft/s. From that point on the lander descended in lunar free fall. (a) What was the impact speed when the lander touched ground (b) How long did it take for the lander to drop the last 4.3ft ( The acceleration of gravity on the moon is 1.62m/S2)

Answer 1

(a) What was the impact speed when the lander touched the ground.

The impact speed is given by

$v=\sqrt[]{2gh}$

Where g is the acceleration of gravity on the moon and h is the distance from the ground.

For the given case,

g = 1.62 m/s^2 = 5.31 ft/s^2

h = 4.3 ft

$v=\sqrt[]{2gh}=\sqrt[]{2\cdot5.31\cdot4.3}=6.76\; \frac{ft}{s}$

The impact speed of the lander is 6.76 ft/s

(b) How long did it take for the lander to drop the last 4.3ft

The time is given by

$\begin{gathered} y=\frac{1}{2}gt^2 \\ 4.3=\frac{1}{2}\cdot5.31\cdot t^2 \\ t^2=\frac{2\cdot4.3}{5.31} \\ t^2=1.6196 \\ t^{}=\sqrt{1.6196} \\ t=1.27\; s \end{gathered}$

Therefore, it takes 1.27 s for the lander to drop the last 4.3 ft