- Suppose that
and . Compute the following quantities.
- Consider the two-dimensional position vector , where
**b**is a positive constant.- Show that the trajectory, or image curve, of is the
circle of radius
**4**centered at the point . That is, show that the component functions and of satisfy the equationfor all values of

**t**. Explain why this means that the image curve is the circle in question. - Show that the speed is constant and explain why this is so. Then
find a value of the constant
**b**that gives a speed of**20**. - Show that is perpendicular to .

- Show that the trajectory, or image curve, of is the
circle of radius
- Suppose particle 1 is going around a circle and its position is
given by . Particle 2,
on the other hand, is going back and forth on the line
**y=ax**with position function , where**a**is a constant.- If
**a=2**, find the value of**t**, , for which the two particles collide. - Is it possible to find a positive real number
**a**for which the two particles do not collide for any value of**t**, ? Explain your answer.

- If
- For the following position vector, determine the value(s) of
**t**, , for which the speed is a minimum.Graphing the speed will allow you to locate the minimum speed approximately, but you should use the techniques from earlier in calculus to find accurate values.

Wed Mar 29 21:31:30 EST 1995