# Homework Help: Particle Intersection Help

1. Jul 30, 2008

### 21omega12

I am very confused about the problem presented below and would appreciate any help in visualization or pointing me in the direction of an article or equation that will set me on the right path. I can't seem to get past the initial set up of the problem at this point and am quite frustrated at the moment.

1. The problem statement, all variables and given/known data
Using a point B, a vector H, and a radius R in 3D space, define a
"pill" as the region within distance R of the line segment between B
and B+H. The pill will be a cylinder of radius R joined with spheres
centered at each of its endpoints. A second point P and vector V define
the motion of a particle: it begins at P at time t=0 and reaches P+V
by t=1.

Calculate the time t (if it is defined and between zero and one) at
which the particle first intersects the pill. This should be an
analytic solution, not a high-level algorithm.

2. Jul 31, 2008

### tiny-tim

Welcome to PF!

Hi 21omega12! Welcome to PF!

B to B+H is a line.

It has a cylinder round it, of radius R, and two hemispheres at the ends.

Hint: If the particle intersects the pill, then it must intersect either the cylinder or one of the hemispheres first.

So just treat it as three separate problems, find t for each problem (if it exists), and then take the minimum of the solutions.