In a perfectly inelastic collision, the two objects stick together after the collision and move as a single combined object.
To solve the problem, we can use the law of conservation of momentum, which states that the total momentum of a system is conserved in the absence of external forces.
Before the collision, the momentum of the motorcycle is:
P1 = m1v1 = 500 kg * 20 m/s = 10000 kgm/s
where m1 is the mass of the motorcycle and v1 is its velocity.
The car is stationary, so its momentum before the collision is:
P2 = m2v2 = 1000 kg * 0 m/s = 0 kgm/s
where m2 is the mass of the car and v2 is its velocity.
The total momentum of the system before the collision is:
P1 + P2 = 10000 kg*m/s
After the collision, the combined mass of the wreckage is:
m = m1 + m2 = 500 kg + 1000 kg = 1500 kg
Let's assume that the wreckage moves at a velocity v after the collision.
By the law of conservation of momentum, the total momentum of the system after the collision is equal to the total momentum before the collision:
P = m*v
P = P1 + P2
10000 kg*m/s = 1500 kg * v
v = 10000 kg*m/s / 1500 kg = 6.67 m/s
Therefore, the velocity of the wreckage after the collision is 6.67 m/s.