One way to measure g on another planet or moon by remote sensing is to measure how long it takes an object to fall a given distance. A lander vehicle on a distant planet records the fact that it takes 3.58 s for a ball to fall freely 12.02 m, starting from rest.

a. What is the acceleration due to gravity on that planet? Express your answer in m/s2. b. What is the acceleration due to gravity on that planet? Express your answer in earth g

(a) 0.94 m/s²

(b) g (planet) = 0.096g

Explanation:

(a)

From Newton's equation of motion,

S = ut + 1/2gt² ... equation 1

Making g the subject of equation 1

g = (S - ut) / t² ... equation 2

Where s = distance (m), u = initial velocity (m/s), t = time (s), g = acceleration due to gravity (m/s²)

From the question, S = 12.02 m, t = 3.58 s, u = 0 (at rest),

Substituting these values in equation 2

g = {12.02 - (0*3.58) }/3.58²

g = (12.02) / 12.82

g = 0.94 m/s²

∴ The acceleration due to gravity on the planet = 0.94 m/s²

(b) g (planet) / g (earth) = 0.94/9.80

g (planet) = 0.096 g (earth).

The acceleration due to gravity of the planet in terms of the earth g is

g (planet) = 0.096g