Question

Two frisky grasshoppers collide in midair at the top of their respective trajectories and grab onto each other, holding tight thereafter. One is a robust 250 g beast initially moving south at 15.0 cm/s, while the other is a svelte 130 g creature initially moving north at 65.0 cm/s.

Calculate the decrease in kinetic energy that results from the collision in J

Answer 1

The decrease in kinetic energy resulting from the collision is 136 J.

Step-by-step explanation:

In this scenario, we have two grasshoppers colliding in midair. To calculate the decrease in kinetic energy resulting from the collision, we need to first calculate the initial kinetic energy of each grasshopper.

The initial kinetic energy of the first grasshopper (mass = 250 g, velocity = -15.0 cm/s) is 93.75 J, and the initial kinetic energy of the second grasshopper (mass = 130 g, velocity = 65.0 cm/s) is 42.25 J. By summing the initial kinetic energies, we find that the total initial kinetic energy is 136 J.

After the collision, the two grasshoppers grab onto each other and move together as one. Therefore, the final kinetic energy of the system is 0 J. The decrease in kinetic energy is therefore given by the difference between the initial and final kinetic energies, which is 136 J - 0 J = 136 J.