A dog of mass 8kg chases a bicycle rider at a speed of 20ms' . The mass of the rider and the bicycle is 48kg and in moving ata speed of 5m-1. if the dog rams and stricks into the spokes of the bicycle, find their common velocity after, and the type of the collision.

Answer 1

We can solve this problem using conservation of momentum:

Initial momentum = Final momentum

The initial momentum is the sum of the momentum of the dog and the momentum of the rider and bicycle:

Initial momentum = (8 kg)(20 m/s) + (48 kg)(5 m/s)
Initial momentum = 160 kg m/s + 240 kg m/s
Initial momentum = 400 kg m/s

After the collision, the dog and the rider and bicycle will move together at a common velocity. We can call this final velocity v.

The final momentum is the momentum of the combined system:

Final momentum = (8 kg + 48 kg)(v)
Final momentum = 56 kg(v)

Equating the initial and final momenta:

Initial momentum = Final momentum
400 kg m/s = 56 kg(v)
v = 7.14 m/s

Therefore, the common velocity after the collision is 7.14 m/s.

To determine the type of collision, we need to look at whether kinetic energy is conserved in the collision. If kinetic energy is conserved, the collision is elastic. If kinetic energy is not conserved, the collision is inelastic.

To find out if kinetic energy is conserved, we can calculate the initial kinetic energy and the final kinetic energy:

Initial kinetic energy = (1/2)(8 kg)(20 m/s)^2 + (1/2)(48 kg)(5 m/s)^2
Initial kinetic energy = 1600 J + 600 J
Initial kinetic energy = 2200 J

Final kinetic energy = (1/2)(56 kg)(7.14 m/s)^2
Final kinetic energy = 1429 J

Since the initial kinetic energy is greater than the final kinetic energy, we know that kinetic energy is not conserved in the collision. Therefore, the collision is inelastic.