Question

suppose the collision between the packages is perfectly elastic. to what height does the package of mass m rebound? (10 pts)

Answer 1

In an elastic collision, the rebound height of the package is the same as its initial height.

Step-by-step explanation:

In elastic collision, both kinetic energy and momentum are conserved.

Using the conservation of momentum, we can calculate the final velocity of the package after the collision.

Let's assume the mass of the package is m and its initial velocity is v. After the collision, the package rebounds with the same speed but in the opposite direction, resulting in a final velocity of -v.

Therefore, the package rebounds to the same height as its initial height.

The conservation of kinetic energy in an elastic collision ensures that the rebound height of the package is the same as its initial height.

Answer 2

In a perfectly elastic collision, the height to which a package rebounds can be calculated using the conservation of energy, equating the kinetic energy at the collision to the potential energy at the rebound's peak.

Step-by-step explanation:

The question is regarding a perfectly elastic collision, which is a concept in physics where two objects collide and bounce off each other without losing any kinetic energy. In the case of a perfectly elastic collision where a package of mass m rebounds, the rebound height can be determined using conservation of energy.

The kinetic energy of the package at the moment of collision is entirely converted to potential energy at the peak of its rebound, allowing us to calculate the maximum height it reaches.

The formula for gravitational potential energy is PE = mgh (where m is the mass, g is the acceleration due to gravity, and h is the height), and for kinetic energy, it's KE = ½mv² (where v is the velocity). Since KE before the collision will equal the PE at the rebound's peak height, we can equate ½mv² = mgh and solve for h, giving h = v² / (2g).