Calculating Momentum of Firing Marksman with X and Y Components

[mikefitz]

These problems with x and y components always leave me confused...

A marksman standing on a motionless railroad car fires a gun into the air at an angle of 30° from the horizontal (the figure below ). The bullet has a speed of 173 m/s (relative to the ground) and a mass of 0.02 kg. The man and car move to the left at a speed of 1.2 " × 10-3 m/s after he shoots. What is the mass of the man and car? [Hint A component of a system's momentum along an axis is conserved if the net external force acting on the system has no component along that axis.]

http://img248.imageshack.us/img248/1495/fig026vo8.gif

I know that momentum is conserved in the form of Pi = Pf. What I don't know is how to calculate the momentums when there are angles involved... Can someone help me get started on this problem please? Thanks

 

[OlderDan]

Before the bullet is fired, the total momentum is zero. After the bullet is fired, the horizontal momentum is zero. The bullet also has vertical momentum, but the car cannot move downward to cancel the vertical bullet momentum, so the total vertical momentum after firing is not zero. All you need to find the solution is to work out the horizontal problem.

 

[kyle8921]

I can understand that problems involving x and y components can be confusing at first. However, with a little bit of practice and understanding of the concepts, you can easily solve these types of problems. Let's break down this problem step by step.

First, let's define what momentum is. Momentum is the product of an object's mass and its velocity, and it is a measure of how much motion an object has. In this problem, we are given the velocity of the bullet (173 m/s) and its mass (0.02 kg), so we can calculate its momentum using the formula p = mv.

Next, we need to consider the motion of the marksman and the railroad car. We are told that they move to the left at a speed of 1.2 x 10^-3 m/s after the gun is fired. This means that the marksman and the car have a common momentum in the x-direction. We can use the same formula (p = mv) to calculate this momentum, but we need to use the combined mass of the marksman and the car.

Now, let's consider the vertical motion of the bullet. The bullet is fired at an angle of 30° from the horizontal, so it has both x and y components of momentum. The x-component of the bullet's momentum is given by p = mv cosθ, where θ is the angle of motion (in this case, θ = 30°). Similarly, the y-component of the bullet's momentum is given by p = mv sinθ.

Since momentum is conserved, we can equate the total momentum of the bullet (in both x and y directions) to the total momentum of the marksman and the car (in the x-direction). This will give us an equation with two unknowns (the mass of the marksman and the car), but we can solve for one of the unknowns using the given information about their combined momentum in the x-direction.

I hope this helps you get started on the problem. Remember to always break down the problem into smaller steps and use the relevant formulas to solve it. With practice, you will become more comfortable with problems involving x and y components.