Question

In an elastic collision, bumper cars 1 and 2 are moving in the same direction when bumper car 1 rear-ends bumper car 2. The initial speed of bumper car 1 is 6.71 m/s and that of bumper car 2 is 4.93 m/s. The bumper cars have the same mass. Take the positive direction to be the direction in which the bumper cars are moving.

What is the final velocity, in meters per second, of bumper car 1?
What is the final velocity, in meters per second, of bumper car 2?

Answer 1

In an elastic collision, the momenta of the two objects are conserved. The initial velocity of bumper car 1 and bumper car 2 are given. By applying the principle of conservation of momentum, we can calculate the final velocities of the bumper cars.

Step-by-step explanation:

In an elastic collision, the momenta of two objects are conserved. The momentum of an object is equal to its mass multiplied by its velocity. So, in this scenario, the initial momentum of bumper car 1, p1 initial, is equal to the final momentum of bumper car 1, p1 final, and the initial momentum of bumper car 2, p2 initial, is equal to the final momentum of bumper car 2, p2 final.

To find the final velocities of the bumper cars, we can use the equation:

m1 * v1 initial + m2 * v2 initial = m1 * v1 final + m2 * v2 final

Substituting the given values, we have:

(m1 * v1 initial) + (m2 * v2 initial) = (m1 * v1 final) + (m2 * v2 final)

Since the bumper cars have the same mass, we can simplify the equation to:

v1 initial + v2 initial = v1 final + v2 final

Now we can substitute the values of the initial velocities to calculate the final velocities.

Answer 2

After an elastic collision between two bumper cars of equal mass and with initial velocities of 6.71 m/s and 4.93 m/s, car 1 will end with a velocity of 4.93 m/s and car 2 with a velocity of 6.71 m/s, as they exchange velocities.

Step-by-step explanation:

In an elastic collision, when two objects of equal mass collide and move in the same direction, their velocities after the collision can be determined using conservation of momentum and conservation of kinetic energy. In the case described, where bumper car 1 with a velocity of 6.71 m/s rear-ends bumper car 2 with a velocity of 4.93 m/s, and both have the same mass, we can apply these principles to calculate the final velocities of the bumper cars.

Since the cars have equal masses, and the collision is elastic, they will simply exchange their velocities. Thus, the final velocity of bumper car 1 (which was moving faster) will be 4.93 m/s, and the final velocity of bumper car 2 will be 6.71 m/s. This outcome is a result of the conservation laws, which dictate that in an elastic collision, the total kinetic energy and the total momentum of the system must remain constant.