A 42-kg girl is bouncing on a trampoline. During a certain interval after leaving the surface of the trampoline, her kinetic energy decreases to 220 J from 460 J. How high does she rise during this interval? Neglect air resistance.

The quarter is over but I am still trying to figure out how to do several problems so that I can know for the next physics class. If you can help that would be great!

Certainly, I can help you with this physics problem!

To find the height to which the girl rises, we need to use the principle of conservation of mechanical energy.

The principle of conservation of mechanical energy states that the total mechanical energy of a system remains constant if no external forces, like air resistance, are acting on it. In this case, the only forces acting are gravity and the trampoline.

The mechanical energy of the girl-trampoline system consists of two types of energy: kinetic energy (KE) and potential energy (PE). Kinetic energy is the energy of motion, and potential energy is the stored energy due to an object's position.

Initially, the girl has a kinetic energy of 460 J. When she reaches the highest point of her motion (when she has stopped momentarily), all her kinetic energy will be converted to potential energy. The potential energy at the highest point is given by the equation:

PE = mgh

where m is the mass of the girl, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.

Now, let's calculate the height by equating the initial kinetic energy to the final potential energy:

KE_initial = PE_final

460 J = mgh

We know the mass of the girl is 42 kg, so substituting the values:

460 J = (42 kg)(9.8 m/s^2)(h)

Simplifying the equation:

460 J = 411.6 kg•m^2/s^2 • h

Dividing both sides by 411.6 kg•m^2/s^2:

h = 460 J / (411.6 kg•m^2/s^2)

h ≈ 1.12 m

Therefore, during this interval, the girl rises approximately 1.12 meters.

I hope this explanation helps you understand the problem! Remember, the key to solving physics problems is utilizing the appropriate equations and principles, and applying them to the given information.