Motion in a Magnetic Field problem

[kjlchem]

Homework Statement

A proton (q = 1.6 X 10-19 C, m = 1.67 X 10-27 kg) moving with constant velocity enters a region containing a constant magnetic field that is directed along the z-axis at (x.,y) = (0,0) as shown. The magnetic field extends for a distance D = 0.7 m in the x-direction. The proton leaves the field having a velocity vector (vx, vy) = (4.3 X 105 m/s, 3.2 X 105 m/s).

What is h, the y co-ordinate of the proton as it leaves the region conating the magnetic field?

Homework Equations

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The Attempt at a Solution

I found R, the curvature of the path, but I have no idea how to find h. I tried using trig and geometry but it didn't work! This is what I did...

h/d=sin(θ)

 

[tiny-tim]

hi kjlchem!

hint: what is the velocity as a function of time?

 

[vivekrai]

You can easily work it out after what tiny has said using calculus.

 

[kushan]

you can easily do with this figure :)

 

[fredrogers3]

you can easily do with this figure :)

I would like to ask something about the diagram. How does one know that the left side of the "square region" has a total length "r?"