Special air bags are used to protect scientific equipment when a rover lands on the surface of Mars. On Earth, the function approximates an object's downward speed in feet per second as the object hits the ground after bouncing x ft in height. The corresponding function for Mars is compressed vertically by a factor of about 2/3. Estimate to the nearest tenth how fast a rover will hit Mars' surface after a bounce of 15 ft in height.

A) 20.7 ft/s

B) 25.3 ft/s

C) 7.3 ft/s

D) 46.5 ft/s

Question

Mathematics

Georgia

7 January, 10:47

Special air bags are used to protect scientific equipment when a rover lands on the surface of Mars. On Earth, the function approximates an object's downward speed in feet per second as the object hits the ground after bouncing x ft in height. The corresponding function for Mars is compressed vertically by a factor of about 2/3. Estimate to the nearest tenth how fast a rover will hit Mars' surface after a bounce of 15 ft in height.

A) 20.7 ft/s

B) 25.3 ft/s

C) 7.3 ft/s

D) 46.5 ft/s

+4

Answers (1)

Know the Answer?

Saul Gaines · Answer 1

The acceleration due to gravity on earth is g = 32.174 ft/s².

Therefore on Mars,

g = (2/3) * 32.174 = 21.45 ft/s²

When an object falls from rest over a distance h, the final velocity, v, obeys the equation

v² = 2gh

or

v = √ (2gh)

Therefore, given h = 15 ft, the impact velocity on Mars is

v = √ (2*21.45*15) = 25.367 ft/s

The closest given answer is 25.3 ft/s

Answer: B) 25.3 ft/s