An arctic village maintains a circular cross country ski tr

An arctic village maintains a circular cross - country ski trail that has a radius of 2.1 kilometers. A skier started skiing from the position (-1.236, 1.6898), measure in kilometers, and skied counter- clockwise for 0.63 Kilometers, where he paused for a brief rest. (Consider the circle to be centered at the origin). Determine the ordered pair (in both kilometers and radii) on the coordinates axes that identifies the location where the skier rested. (x, y) = () radii (x, y) = (, )kilometers

Solution

The circumference of the trail is C = 2(pi)r = 2*pi*2.1 km=4.2pi

Befor stoping the skier stied 0.63 km before coming to rest

=0.63/(4.2pi)

therfore angle skied=(0.63/(4.2pi))*2pi)=0.63/2.1=0.3 radian

Now since the The skier has gone 0.3 radians from ( -1.236,1.698 )

new position x=rcos(theta)=2.1cos(0.3 rad)=2.006

and y=rsin(theta)=2.1sin(0.3 rad)=0.6206