Fireworks Problem: Find Speed & Distance of Fragments

• iwonde
In summary, the problem involves a fireworks rocket exploding at its maximum height of 80.0 m and breaking into two pieces with masses of 1.40 kg and 0.28 kg. The explosion converts 860 J of chemical energy into kinetic energy of the two fragments. The task is to find the speed of each fragment after the explosion and the distance between the points on the ground where they land. To solve this, we can use the equation MV_cm = P for the center of mass and (1/2)(m_1 + m_2) v^2 = 860 J for the conservation of energy. The second equation should include both unknown velocities.
iwonde

Homework Statement

A fireworks rocket is fired vertically upward At its maximum height of 80.0 m, it explodes and breaks into two pieces, one with mass 1.40 kg and the other with mass 0.28 kg. In the explosion, 860 J of chemical energy is converted to kinetic energy of the two fragments.
(a) What is the speed of each fragment just after the explosion?
(b) It is observed that the two fragments hit the ground at the same time. what is the distance between the points on the ground where they land? Assume that the ground is level and air resistance can be ignored.

Center of Mass:
MV_cm = P

The Attempt at a Solution

I don't know how to approach this problem.

What the firework's velocity at its maximum height? Its momentum?

After it explodes, what is the sum of the two objects momenta?

If you can answer those questions, you should be able to write an equation including both unknown velocities. Then see if you can find a second equation given the information in the problem.

The velocity at the maximum height is zero, so it's momentum at that point is zero.

After it explodes: (m_1)(v_1)+(m_2)(v_2) = 0
From the problem, (1/2)(m_1 + m_2) v^2 = 860 J
I'm trying to solve for v_1 and v_2.

Is my second equation correct?

The 860J goes into both fragments, so you have two velocities in the second equation, not one.

1. How do you calculate the speed of a firework fragment?

The speed of a firework fragment can be calculated by dividing the distance it travels by the time it takes to travel that distance. This is known as the average speed formula: speed = distance/time.

2. What is the distance of a firework fragment?

The distance of a firework fragment can be measured by using a ruler or measuring tape to determine the distance it travels from the launch point to where it lands. This distance can then be used in the speed calculation.

3. How can you find the time it takes for a firework fragment to travel?

The time it takes for a firework fragment to travel can be determined by using a stopwatch or timer to record the time it takes for the fragment to travel from the launch point to where it lands. This time can then be used in the speed calculation.

4. What factors can affect the speed and distance of firework fragments?

The speed and distance of firework fragments can be affected by factors such as wind speed and direction, the angle of launch, and the type and amount of propellant used in the firework.

5. How accurate are the calculations for the speed and distance of firework fragments?

The accuracy of the calculations for the speed and distance of firework fragments depends on the precision of the measurements taken and the accuracy of the average speed formula used. Variations in environmental factors and the design of the firework can also affect the accuracy of the calculations.

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