Calculating Vector Velocity in a Nuclear Reaction: Homework Problem

[bobsmith76]

Homework Statement

Consider a nuclear reaction in which a neutron traveling 1.0 × 10⁷ m/s in the +x direction collides with a proton traveling 5.0 × 10⁶ m/s in the +y direction. They combine at impact to form a new particle called a “deuteron.” What is the magnitude of the deuteron velocity? Assume for simplicity that the proton and neutron have the same mass.

Homework Equations

a² + b² = c²

The Attempt at a Solution

I would think you would just use the pythagorean theorem to solve the problem. When you do that you get 1.1 * 10⁷ The textbook says the answer is 5.6 * 10⁶

 

[Doc Al]

I would think you would just use the pythagorean theorem to solve the problem.

You'd use the Pythagorean theorem to add the two momenta. But how would you solve for the new velocity?

 

[bobsmith76]

But if their mass is the same then the momentum should equal the velocity. In the equation

p = mv

If m = 1, then p should equal v

 

[Doc Al]

But if their mass is the same then the momentum should equal the velocity. In the equation

p = mv

If m = 1, then p should equal v

If the mass of each original particle is '1' unit, what's the mass of the new combined particle?

 

[bobsmith76]

Thanks, I got it. I really appreciate your help.