posted by Frances on .
The method by which the Mars exploration rovers, Spirit and Opportunity, landed on the surface of Mars in January of 2004 was quite elaborate. The rovers began their descent through the thin Martian atmosphere on a parachute until they reached an altitude of about 16.7 m. At that point a system of four air bags with six lobes each were inflated, retro rockets
brought the craft to rest, and the rovers detached from their parachutes.
After free-falling to the surface, with an acceleration of 3.72 m/s^2, and bouncing about a dozen times, the rovers deflated their air bags, righted themselves, and went about their explorations. On the first bounce from the surface, the rovers had an initial velocity of 9.92 m/s at an angle of 75.0
degrees above the horizontal. (A) What was the maximum height of a rover between the first and second bounces? (B) How far did a rover travel in the horizontal direction between the first and second bounces?
(A) Use the vertical component of the initial bounce velocity (9.92 m/s*sin 75) and the acceleration of gravity near the Martian surface (3.72 m/s^2) to get the time in the air during the first bounce, and the maximum height.
(B) Multiply the time you get in (A) by the horizontal velocity component, 9.92 m/s* cos 75.