Final answer:
The change in velocity on the bug is approximately 17.65 m/s.
Step-by-step explanation:
In this problem, we have an elastic collision between a bug and a car. To find the change in velocity on the bug, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
The momentum formula is mass multiplied by velocity: momentum = mass x velocity.
The momentum of the bug initially is 0 kg m/s because its initial velocity is zero. The momentum of the car initially is the product of its mass (1500 kg) and its initial velocity (20 m/s), which is 30000 kg m/s.
After the collision, the bug and the car travel together with the same velocity. Let's call this final velocity V. The combined mass is the sum of the bug's mass and the car's mass, which is 200 kg + 1500 kg = 1700 kg. The momentum after the collision is the product of the combined mass and the final velocity, which is 1700 kg x V.
Using the principle of conservation of momentum, we equate the momentum before the collision to the momentum after the collision:
30000 kg m/s = 1700 kg x V
Solving for V, we find that the final velocity of the bug and the car is approximately 17.65 m/s.
Therefore, the change in velocity of the bug is the final velocity (17.65 m/s) minus its initial velocity (0 m/s), which is equal to approximately 17.65 m/s.