The 2004 landings of the mars rovers spirit and opportunity involved many stages, resulting in each probe having zero vertical velocity about 12 m above the surface of mars. determine
(a) the time required for the final free-fall descent of the probes
(b) the vertical velocity at impact. the mass of mars is 6 . 419 × 10 23 kg , and its radius is 3 . 397 × 10 6 m

2.54334 seconds

9.4364 m/s

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration

g = Acceleration due to gravity

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

M = Mass of Mars =

R = Radius of Mars =

The acceleration due to gravity of a planet is given by

Equation of motion

The time taken to fall 12 m in Mars is 2.54334 seconds

The vertical velocity at impact is 9.4364 m/s

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.