# Velocities and momentum after explosions

• Delta Sheets
In summary, a 5.43-kg bowling ball with an initial speed of 12.9 m/s at a 39.9° angle is launched into the air with several firecrackers and explodes into three pieces of equal mass. One piece travels straight up with a speed of 3.83 m/s and another travels straight back with a speed of 1.71 m/s. Using the conservation of momentum equation, the velocity of the third piece is calculated to be 31.63 m/s. However, when attempting to find the direction of this velocity using the tangent inverse, the answer was incorrect. Further help is needed to determine the correct momentum of the third piece.
Delta Sheets

## Homework Statement

After several large firecrackers have been inserted into its holes, a bowling ball is projected into the air using a homemade launcher and explodes in midair. During the launch, the 5.43-kg ball is shot into the air with an initial speed of 12.9 m/s at a 39.9° angle; it explodes at a peak of its trajectory, breaking into three pieces of equal mass. One piece travels straight up with a speed of 3.83 m/s. Another piece travels straight back with a speed of 1.71 m/s.

a) What is the velocity of the third piece?

b) What is the direction of the velocity of the third piece?

## Homework Equations

Momentum is conserved
m1v1 + m2v2 + m3v3(initial)=m1v1 + m2v2 + m3v3(final)

## The Attempt at a Solution

I figured since there is no momentum in the y direction at the time of explosion, the y momentum going up must equal the y momentum going down, which is 6.93 kg*m/s.
With this is took the momentum of the third piece (31.63)(1.81)= 57.25 kg*m/s, then used the tangent inverse tan^-1(-6.93/57.25) to find the angle, but it did not give me the right answer.

I assume the mistake I made was with the momentum of the third piece, but I am not sure what it should be. Any help is greatly appreciated.

## 1) What is the difference between velocity and momentum?

Velocity is the rate of change of an object's position over time, and is measured in meters per second (m/s). Momentum is the product of an object's mass and its velocity, and is measured in kilogram meters per second (kg*m/s).

## 2) How do velocities and momentum change after an explosion?

After an explosion, the velocities and momentum of objects involved will change based on the amount and direction of the force exerted by the explosion. The objects will accelerate in the direction of the force, resulting in changes in their velocities and momentum.

## 3) Can an object have a high velocity but low momentum after an explosion?

Yes, an object can have a high velocity but low momentum if its mass is relatively small. This is because momentum takes into account both the speed and mass of an object, so a small mass would result in a lower overall momentum despite a high velocity.

## 4) How do you calculate the momentum of an object after an explosion?

Momentum can be calculated by multiplying the mass of an object by its velocity. In an explosion scenario, the total momentum of all the objects involved before and after the explosion will remain constant, as long as there are no external forces acting on the system.

## 5) Can the velocity of an object after an explosion be greater than the speed of light?

No, according to the theory of relativity, nothing can travel faster than the speed of light. This means that the velocity of an object after an explosion cannot exceed the speed of light, regardless of the force exerted by the explosion.

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