Question

Tom's 100kg bumper car is traveling east at 10 m/s when it collides head-on with Ray's 80kg bumper car traveling west. After the collision, Tom's car

travels west at 20m/s while Ray's travels east at 15m/s. Determine Ray's initial velocity

Answer 1

The initial momentum of the system is the sum of the individual momenta of Tom and Ray before the collision. Using the conservation of momentum equation, we can determine Ray's initial velocity to be approximately 0.2875 m/s.

Step-by-step explanation:

When two objects collide, the sum of their momentum before the collision is equal to the sum of their momentum after the collision, assuming no external forces are involved.

To find Ray's initial velocity, we can use the principle of conservation of momentum. The initial momentum of the system is the sum of the individual momenta of Tom and Ray before the collision. Since Tom is moving east at 10 m/s and Ray is moving west, we can represent their velocities as +10 m/s and -v m/s respectively.

Using the conservation of momentum equation:
Initial Momentum = Final Momentum

(100 kg)(10 m/s) + (-80 kg)(-v m/s) = (100 kg)(-20 m/s) + (-80 kg)(15 m/s)

Simplifying the equation, we get:
(1000 kg m/s) + (80 kg m/s) = (-2000 kg m/s) + (-1200 kg m/s)

Combining like terms, we obtain:
-920 kg m/s = -3200 kg m/s

Dividing both sides by -3200 kg m/s, we get:
v = 0.2875 m/s

Therefore, Ray's initial velocity is approximately 0.2875 m/s.