While attempting a landing on the moon, astronauts had to change their landing site and land at a spot that was 4 kilometers away from the original site. Assuming that they were at a height of 137 meters, calculate the horizontal velocity of the spacecraft during touchdown if it lands in a free-fall mode without using retro engines. Consider gravity = 1.63 meters/second2.

Question

Physics

Nataly Spears

19 June, 10:19

While attempting a landing on the moon, astronauts had to change their landing site and land at a spot that was 4 kilometers away from the original site. Assuming that they were at a height of 137 meters, calculate the horizontal velocity of the spacecraft during touchdown if it lands in a free-fall mode without using retro engines. Consider gravity = 1.63 meters/second2.

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Grant Frye · Answer 1

Refer to the figure below.

A = original landing site.

B = alternate landing site.

Assume that aerodynamic resistance is negligible.

The craft lands in free-fall mode, therefore its original vertical velocity is zero.

It travels downward by 137 m at gravitational acceleration of g = 1.63 m/s².

The time of travel, t, obeys the equation

(137 m) = (1/2) (1.63 m/s²) * (t s) ²

Therefore

t² = (137*2) / 1.63 = 168.098 = > t = 12.965 s.

The constant horizontal velocity, u, required to travel 4 km (or 4000 m) in time, t, is given by

(u m/s) * (12.965 s) = (4000 m)

u = 4000/12.965 = 308.5 m/s (nearest tenth)

Answer: 308.5 m/s