# Find the Ratio: Solving Recoil Speed in Homework Equations

In summary, a person standing on a slippery ice fires a gun parallel to the ground. When using a standard cartridge, a 13-g bullet is shot forward with a speed of 290 m/s and the person recoils with a speed of vc. With a blank cartridge, a 0.13g mass is shot forward at 53 m/s and the person recoils with a speed of vb. To find the ratio vb/vc, the law of conservation of momentum can be used by setting the initial momentum of the system to zero and solving for the velocities of the bullet and person. This can be done by writing two equations for the standard and blank cartridges and solving for vc and vb.

## Homework Statement

A person is standing on a sheet of ice so slippery that friction may be ignored. This individual fires a gun parallel to the ground. When a standard cartridge is used , a 13-g bullet is shot forward with a speed of 290 m/s, and the person recoils with a speed of vc. When a blank cartridge is used , a mass of 0.13g is shot forward with a speed of 53 m/s , and the recoil speed is vb. Find the ratio vb/vc.

## Homework Equations

I tried to use P= p1+p2
I got
P1=13*Vc
P2=.13*Vb
Ended with 13Vc+.13Vb
I am sooo confused. Its asking for the ratio and its totally throwing me off. Plus I am not even sure I am using the right formula or if I understand the question properly

## The Attempt at a Solution

Initially person and the gun are at rest.So the total momentum of the system is zero.
When the gun is fired, bullet moves forward with some velocity and person recoils. Find the momentum of each and add them. According to the law conservation of momentum the sum should be zero.
Write down two equations, one for standard cartridge and other for blank cartridge. Then find of vc and vb.

Im sorry, I don't understand. I am a beginner at physics and don't have a good basis. Was I on the right track. If not, can you demonstrate what ur saying

nevermind...got it

## What is the formula for finding recoil speed in homework equations?

The formula for finding recoil speed in homework equations is: recoil speed = (mass of object * velocity of object) / mass of gun.

## How do I know which values to use for the mass and velocity of the object and gun in the recoil speed formula?

The values for the mass and velocity of the object and gun should be given in the problem or can be obtained from other given information. Make sure to use consistent units for all values.

## Can I use this formula to find the recoil speed for any type of object and gun?

Yes, this formula can be used to find the recoil speed for any type of object and gun, as long as the necessary values are known.

## What are the units for the recoil speed in this formula?

The units for the recoil speed will depend on the units used for the mass and velocity of the object and gun. Make sure to use consistent units and convert if necessary.

## What are some common mistakes to avoid when using this formula to find recoil speed?

Some common mistakes to avoid when using this formula include using incorrect units, not using the correct values for the mass and velocity of the object and gun, and not considering the direction of the recoil. It is important to carefully read and understand the problem before plugging in values to the formula.

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