Question

A 1.5-kg object traveling at 6.1 m/s collides head-on with a 5.0-kg object traveling in the opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final velocity (in m/s) of the 1.5-kg object?

Answer 1

To find the final velocity of the 1.5-kg object after an elastic collision with a 5.0-kg object, apply the conservation laws for momentum and kinetic energy. Solve the system of equations algebraically to determine the object's final velocity.

Step-by-step explanation:

The question involves solving for the final velocity of a 1.5-kg object after a perfectly elastic collision with a 5.0-kg object, where both objects are traveling in opposite directions. An elastic collision is a type of collision where both momentum and kinetic energy are conserved. Using the conservation of momentum and kinetic energy principles, we can set up the following equations:

• Conservation of momentum: m1v1i + m2v2i = m1v1f + m2v2f

• Conservation of kinetic energy: (1/2)m1(v1i)2 + (1/2)m2(v2i)2 = (1/2)m1(v1f)2 + (1/2)m2(v2f)2

Substitute the known values into these equations and solve for the final velocity v1f of the 1.5-kg object. This involves algebraic manipulation and possibly the use of a quadratic equation to find the solution. The question requires understanding of concepts such as momentum, kinetic energy, and elastic collisions.