What are the masses of two objects given their velocities and total momentum?

[MarineBio]

Homework Statement

Object 1 has a mass m1 and a velocity 1 = (2.70 m/s) on the x-axis. Object 2 has a mass m2 and a velocity 2 = (2.95 m/s) on the y-axis. The total momentum of these two objects has a magnitude of 18.6 kg·m/s and points in a direction 66.5° above the positive x-axis. Find m1 and m2.

The Attempt at a Solution

I honestly don't even know where to begin. I am finding it impossible to determine mass 1 and mass 2 without knowing one or the other. How do I even set this one up?

 

[alphysicist]

Hi MarineBio,

Homework Statement

Object 1 has a mass m1 and a velocity 1 = (2.70 m/s). Object 2 has a mass m2 and a velocity 2 = (2.95 m/s). The total momentum of these two objects has a magnitude of 18.6 kg·m/s and points in a direction 66.5° above the positive x-axis. Find m1 and m2.

The Attempt at a Solution

I honestly don't even know where to begin. I am finding it impossible to determine mass 1 and mass 2 without knowing one or the other. How do I even set this one up?

Was there some more information given, perhaps in a diagram? (For example, showing that mass 1 goes along the x-axis and mass 2 goes along the y-axis, or something like that.)

I'm surprised that they would say the velocity is 2.7m/s (for example) without giving a direction or a unit vector. If they did not give a direction, it seems like they would have referred to it as just the speed.

 

[MarineBio]

Hi MarineBio,



Was there some more information given, perhaps in a diagram? (For example, showing that mass 1 goes along the x-axis and mass 2 goes along the y-axis, or something like that.)

I'm surprised that they would say the velocity is 2.7m/s (for example) without giving a direction or a unit vector. If they did not give a direction, it seems like they would have referred to it as just the speed.

Shoot, when I copy/pasted it did not include the x and y hats.

V1 is on the x axis
V2 is on the y axis

 

[jgens]

That makes things relatively simple! Since momentum is a vector quantity the component in the x and y directions should be: 18.6cos(θ) and 18.6sin(θ) respectively. Just resolve the components!

Since V₁ is on the x-axis: m₁V₁ = 18.6cos(θ)

A similar argument can be made for the y-axis component.

 

[alphysicist]

Shoot, when I copy/pasted it did not include the x and y hats.

V1 is on the x axis
V2 is on the y axis

Okay, then you can add up the momentum: the momentum of m1 + momentum of m2 = total momentum.

Remember though that since momentum is a vector quantity, and this is a 2-D problem, you'll end up needing to have a momentum equation for the x-direction, and a momentum equation for the y-direction.

Does that help? If not, please post what you are trying.

 

[MarineBio]

That makes things relatively simple! Since momentum is a vector quantity the component in the x and y directions should be: 18.6cos(θ) and 18.6sin(θ) respectively. Just resolve the components!

Since V₁ is on the x-axis: m₁V₁ = 18.6cos(θ)

A similar argument can be made for the y-axis component.

Ha! I was making that one WAY more difficult than it actually was. Thank you, problem solved!

(this is such a great forum)