The following is a hypothetical approach to the next generation of mars exploration. a landing craft hovers 220 m above the martian surface. the craft drops a 40kg mini rover, which deploys an airbag before it hits. as it crashes down, it compresses the airbag by 5 cm (maximum), and then it bounces back up in the thin martian air to a height of 20 m before finally coming to rest on the surface. following the completion of its tasks, another craft comes overhead at the same height, and drops a line that attaches to the rover. it then uses a 2 kw motor to pull the rover up to the mother ship. note that the acceleration of gravity on mars is 3.7 m/s2 and the mass of mars is 6.4 x 1023 kg.
1. at what speed would the rover have hit mars had the airbag not been used?
(a) 4m/s
(b)12m/s
(c)40m/s
(d)66m/s
(e)1.6x103m/s

2. what percent of the mechanical energy is absorbed by the airbag and therefore lost?

(a) 0%
(b) 9%
(c) 91%

3. how much work is done raising the rover?
(a)3.3x104j
(b)8.6x104 j
(c)2x103 j

4. how long does it take to pull the rover up?
(a) 0.06 sec
(b) 16.5 sec
(c) 43 sec
5. what is the radius of mars?
(a)3.7x106 m
(b)1.15x106 m
(c)2x106 m
6. how much force does mars exert on the rover while it is being lifted?
(a)0n
(b)88lb
(c)148n
(d)392n
7. if the airbag functions like a giant spring as it is compressed, and you wanted it now to absorb twice as much energy, it would then be squashed at maximum compression by
(a) 5cm
(b)7cm
(c)10cm
(d)14cm
(e)20cm