The equation for free fall at the surfaces of Mars and Jupiter (s in meters , t in seconds) are s = 1.86t^2 on mars and s=11.44t^2 on Jupiter. How long does it take a rock falling from rest to reach a velocity of 27.8 m/sec on each planet?
The equation for free fall on Mars is s = 1.86*t^2 where s is the velocity in m/s and t is the time in seconds.
Let the time taken for an object that is dropped to reach 27.8 m/s be T
=> 27.8 = 1.86*T^2
=> T^2 = 27.8/1.86
=> T = sqrt(27.8/1.86)
=> T = 3.866 seconds
Similarly the relation between velocity and time on Jupiter is s = 11.44*t^2.
The time it takes for a rock dropped on Jupiter to reach 27.8 m/s is calculated as:
27.8 = 11.44*T^2
=> T^2 = 27.8/11.44
=> T = sqrt(27.8/11.44)
=> T = 1.55 seconds
The time it takes a rock to reach 27.8 m/s on Mars is 3.866 s and on Jupiter it takes 1.55 s.