Dr. Parsons pedals his Mini Cooper for 5 km at an angle of 42 degree North of We

Question

Dr. Parsons pedals his Mini Cooper for 5 km at an angle of 42 degree North of West. He then pedals it for 6 km at an angle of 22 degree West of South. Dr. Martin pushes his BMW in a straight line from Dr. Parsons' starting point to where Dr. Parsons ends. a. How far west is Dr. Parsons from his starting point? (include units with answer) B. How far did Dr. Martin push his Bimmer? (include units with answer) C. At what angle did Dr. Martin push his Bimmer? Express the answer in terms of the angle counterclockwise (CCW) from the x-axis, where the positive x-axis is in the East direction and the positive y-axis is in the North direction (include units with answer)

Explanation / Answer

A] west distance = 5 cos 42 degree + 6 sin 22 degree

= 5 96 km answer

b] south distance =  -5 sin 42 degree + 6 cos 22 degree = 2.22 km

distance travelled by Dr. Martin = sqrt(5.96^2+2.22^2) = 6.36 km answer

c] angle = 180 degree + arctan(2.22/5.96)=180+20.43 = 200.43 degree answer

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