**Sample Problem**

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn. The coordinates of the rabbit’s position as functions of time 1 are given by

with in seconds. and A and y in meters

(a) At what is the rabbit’s position vector Pin unit vector notation and as a magnitude and an angle

SOLUTION: The Key idea here is that the x and y coordinates of the rabbit’s position, as given by scalar components of the rabbit’s position vector. Thus, we can write

(Although (J = 139° has the same tangent as 41°, study of the signs of the components of rules out 139°.)

(b) Graph the rabbit’s path for 1 = 0 to 1 = 25 s.

SOLUTION: We can repeat part (a) for several values of 1 and then plot the results. Shows the plots for five values of I and the path connecting them. We can also use a graphing calculator to make e parametric graph: that is, we would have the calculator plot y versus x, where these coordinates are given by as functions of time .

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