What is the Final Momentum of Three Colliding Balls?

[ScullyX51]

Homework Statement

A red ball is heading due east, a blue ball is moving due west, and a green ball is moving north. They have initial speeds vr,i=20 cm/s, vb,i=10 cm/s, vg,i=10 cm/s. The red ball has a mass of 5 g, the blue ball has a mass of 10g, and the green ball has a mass of 5g. The three balls all collide, and stick together. Find the magnitude and direction of the final momentum of the composite.

Homework Equations

the sum of P_I=the sum of P_F

The Attempt at a Solution

Ok...without plugging the numbers in this is what I have so far:
I don't really know how to approach this problem, so if someone could tell me if I am starting it on the right path would be great.
I broke it up into x and y components, and for the x component of momentum I have:
M_BV_B-M_RV_R=(M_R+M_B+M_G)V_FX)

Then for the y component I have:
M_GV_G=(M_R+M_B+M_G)V_FY)

Am I on the right track...or completely missing the point?

 

[tiny-tim]

Hi ScullyX51!

Ok...without plugging the numbers in this is what I have so far:
I don't really know how to approach this problem, so if someone could tell me if I am starting it on the right path would be great.
I broke it up into x and y components, and for the x component of momentum I have:
M_BV_B-M_RV_R=(M_R+M_B+M_G)V_FX)

Then for the y component I have:
M_GV_G=(M_R+M_B+M_G)V_FY)

Am I on the right track...or completely missing the point?

Yes, that is exactly the right track …

momentum is a vector, and so it obeys the laws of vector addition …

sometimes physics is that easy!

 

[thomate1]

Yes, you are on the right track with your approach. To find the final momentum of the composite, you will need to use the conservation of momentum principle, which states that the total momentum before a collision is equal to the total momentum after the collision. This means that the sum of the initial momentums of the three balls (red, blue, and green) must be equal to the sum of the final momentum of the composite.

To solve this problem, you will need to first calculate the initial momentum of each ball separately, using the formula P=mv, where P is momentum, m is mass, and v is velocity. Then, you can use the conservation of momentum principle to set up equations for the x and y components of momentum, as you have already done.

Once you have these equations, you can solve for the final velocity of the composite in each direction (x and y) by plugging in the initial velocities and masses of the three balls. The final momentum of the composite will then be the vector sum of these two velocities, which you can find using the Pythagorean theorem.

Remember to pay attention to the direction of the final momentum. Since the red and blue balls are moving in opposite directions, their x components of momentum will cancel out, leaving only the y components to contribute to the final momentum in that direction. The final direction of the composite's momentum can be found by using the inverse tangent function to find the angle of the resulting vector.

I hope this helps guide you in solving the problem. Good luck!