score in gradebook: 0.3 out of 1 Reattempt last question below, or select anothe

Question

score in gradebook: 0.3 out of 1 Reattempt last question below, or select another question An arctic village maintains a circular cross-country ski trail that has a radius of 3.2 kilometers. A skier started skiing from the position (0093,3.199), measured in kilometers, and skied counter clockwise for 0.96 kilometers, where he paused for a brief rest (Consider the circle to be centered at the origin). Determine the ordered pait (in both kilometers and radn) the coordinate axes that identifies the location where the skier rested Hint Start by drawing a diagram to represent this situation 0.955 radin kilometer License Points possible: 1 Unlimited attempts Score on last attempt 03 Score in gradebook 03 Submit

Explanation / Answer

Skier started from point (-0.093, 3.199)

As per question, Circle is at center(0,0). Circle cuts positive x-axis at point( radius, 0 ) = > ( 3.2 , 0)

Let Initial angle made by skier from the point it started with positive x-axis be s

We know from figure 1

rcos(s)= -0.093 ----- 1st equation

rsin(s) = 3.199 ----- 2nd equation

dividing equations 2 by 1

=> rsin(s)/rcos(s)=tan(s) = 3.199/-0.093 = - 34.3978

sin(s) is +ve , cos(s) is -ve , tan(s) is also -ve

it means that angle lies in 2nd quadrant

=> s= pi - arctan(34.3978) = pi - 1.54173289 =pi - 1.54173289 = 1.59985976 radians

this is the initial angle made by skier

Now , he has travelled 0.96 km before resting

=> angle made at resting point from starting point by skier = u = distance covered / radius = 0.96/3.2 = 0.3 radians

=> (z)total angle made at reting point with respect to +ve x axis = z = s + u = 1.59985976 + 0.3 = 1.89985976 radians

Resting point coordinates ( radii) = ( cos(z) ,sin(z) ) = ( cos( 1.89985976), sin(1.89985976) ) = ( -0.32315685, 0.94634542)

Resting point coordinates ( km) = ( rcos(z) ,rsin(z) ) = ( rcos( 1.89985976), rsin(1.89985976) ) =(-1.03410192, 3.028305344)

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