Question

At the peak of its trajectory, a 995-g fireworks rocket is moving horizontally at 18.6 m/s. It’s a dud, and instead of exploding gloriously, it bursts into two pieces. One of them, with mass 352 g, continues in the original direction at 31.3 m/s.How much energy did the two pieces gain when the rocket burst?

Answer 1

To determine the energy gained by two rocket pieces post-explosion, we apply the conservation of momentum and kinematic equations to find their velocities and then calculate the change in kinetic energy.

Step-by-step explanation:

The question involves calculating the energy gained when a 995-g fireworks rocket bursts into two pieces at the peak of its trajectory, with one piece of 352 g continuing in the original direction at 31.3 m/s. To determine the energy gained, we must use the principles of conservation of momentum and the kinematic equations describing the motion of the rocket pieces. We initially have the total kinetic energy of the intact rocket, which we can compare to the kinetic energy of the two pieces after the explosion.

Let's start with the conservation of momentum:

Initial momentum = final momentum
(m_total * v_total) = (m_piece1 * v_piece1) + (m_piece2 * v_piece2)

Given the mass and velocity of piece 1, we can rearrange the formula to solve for the velocity of piece 2. After finding the velocities of both pieces, we assess the kinetic energy:

KE = (1/2) * m * v^2

We calculate the kinetic energy of both pieces post-explosion and compare it to the kinetic energy of the rocket before the explosion. The difference in energy will provide us with the energy gained during the burst.