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## Homework Statement

A particle of mass

*m*moving with velocity

**v**

_{1}leaves a half-space in which its porential energy is a constant

*U*

_{1}and enters another in which its potential energy is a different constant

*U*

_{2}.

Determine the change in the direction of motion of the particle.

## Homework Equations

The porential energy is independent of the co-ordinates whose axes are parallel to the plane separating the half-spaces. The component of momentum in that plane is therefore conserverd. Denoting by

*θ*

_{1}and

*θ*

_{2}the angles between the normal to the plane and the velocities

**v**

_{1}and

**v**

_{2}of the particle before and after passing the plane, we have

*v*

_{1}sin

*θ*

_{1}=

*v*

_{2}sin

*θ*

_{2}. The relation between

*v*

_{1}and

*v*

_{2}is given by the law of conservation of energy, and the result is

## The Attempt at a Solution

I have no idea what a situation of the problem is.

Is the situation of the problem this?

If so, is a direction of force vertical to the paper?

And why

*v*

_{1}sin

*θ*

_{1}=

*v*

_{2}sin

*θ*

_{2}?