The answer to Why a rover bounces after landing on Mars? is "the Mars Exploration Rovers" of which there were two.
However, they might not be the only spacecraft to use bouncing like a ball to absorb the final few m/s of speed and bring the spacecraft to rest.
Question: How many spacecraft bounced like a ball on Mars? How many at least planned to do so?
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The Mars Pathfinder mission, which landed on Mars in 1997, used inflatable bags.
The bags were inflated when Pathfinder was 355 m above the ground.
Once the lander was 355 m above the ground, airbags were inflated in less than a second using three gas generators. The airbags were made of four inter-connected multi-layer vectran bags that surrounded the tetrahedron lander. They were designed and tested to accommodate grazing angle impacts as high as 28 m/s. However, as the airbags were designed for no more than about 15 m/s vertical impacts, three solid retrorockets were mounted above the lander in the backshell. These were fired at 98 m above the ground. The lander's on-board computer estimated the best time to fire the rockets and cut the bridle so that the lander velocity would be reduced to about 0 m/s between 15 and 25 m above the ground. After 2.3 seconds, while the rockets were still firing, the lander cut the bridle loose about 21.5 m above the ground and fell to the ground. The rockets flew up and away with the backshell and parachute (they have since been sighted by orbital images). The lander impacted at 14 m/s and limited the impact to only 18 G of deceleration. The first bounce was 15.7 m high and continued bouncing for at least 15 additional bounces (accelerometer data recording did not continue through all of the bounces).
Once the lander stopped rolling, the airbags deflated and retracted toward the lander using four winches mounted on the lander "petals". Designed to right itself from any initial orientation, the lander happened to roll right side up onto its base petal.
The other US landers to have used air bags were Spirit and Opportunity, all three being US missions.
The only Soviet soft landing on Mars was the Mars 3 probe, which failed 110 seconds after landing.
The Mars 3 descent module was mounted on the bus/orbiter opposite the propulsion system. It consisted of a spherical 1.2 m diameter landing capsule, a 2.9 m diameter conical aerodynamic braking shield, a parachute system and retro-rockets.
Mars 3's descent module was released at 09:14 UT on December 2, 1971, 4 hours 35 minutes before reaching Mars. The descent module entered the Martian atmosphere at roughly 5.7 km/s. Through aerodynamic braking, parachutes, and retrorockets, the lander achieved a soft landing at 45°S 202°E Coordinates: 45°S 202°E and began operations.
Soviet missions Mars 2, Mars 6 and Mars 7 and the Russian Mars 96 all failed to achieve a soft landing.
It was intended for Mars 96 to deploy airbags at an altitude of 17.9 km.
While the orbiter performed the orbit insertion burn, both Surface Stations were to make a soft landing on Mars. Both landing sequences were identical. They began with the craft being slowed down by aerodynamic pressure. At an altitude of 19.1 km, a parachute would deploy, followed by heat shield separation at 18.3 km, and inflation of the airbags at 17.9 km. When the lander, cushioned by the airbags, hit the ground, the parachute would separate. The airbag would eventually roll to a stop. After which both airbags would separate revealing the lander. The four petals would open and the lander would signal the orbiter when it passed over the landing site.
The failed Beagle 2 mission (part of ESA's Mars Express mission) also used airbags:
After deceleration in the Martian atmosphere, parachutes deployed, and at about 200 m above the surface large airbags inflated around the lander to protect it when it hit the surface. Landing occurred at about 02:45 UTC on 25 December 2003.
