- 25

- 0

**1. Homework Statement**

A particle moves down with position vector <sec(Pi*t), tan(Pi*t)> for

0 =< t < 1/2.

(a). Find the velocity and speed of the particle at t = 1/4.

(b). The particle movies along a hyperbola. Elminate the parameter to find an equation of the hyperbola in terms of x and y.

(c). Sketch the path of the particle over the time interval

0 =< t < 1/2.

**2. Homework Equations**

? none?

**3. The Attempt at a Solution**

velocity vector = < Pi*sec(Pi*t)tan(Pi*t), Pi*sec^2(Pi*t)>

Plug in 1/4 into velocity vector:

<.04307, Pi>

Question is (part a), it's asking for velocity. I'm thinking writting velocity vector isn't the same thing; should I do a pythagorean theorem on the two components of my velocity vector to get a single value for velocity?

Help appreciated :P