You are kidnapped by political-science majors (who are upset because you told th

Question

You are kidnapped by political-science majors (who are upset because you told them political science is not a real science). Although blindfolded, you can tell the speed of their car (by the whine of the engine), the time of travel (by mentally counting off seconds), and the direction of travel (by turns along the rectangular street system). From these clues, you know that you are taken along the following course: 50 km/h for 2.0 min, turn 90° to the right, 20 km/h for 3.0 min, turn 90° to the right, 20 km/h for 60 s, turn 90° to the left, 40 km/h for 70 s, turn 90° to the right, 20 km/h for 2.0 min, turn 90° to the left, 40 km/h for 30 s. At that point, (a) how far are you from your starting point, and (b) in what direction relative to your initial direction of travel are you? Give your answer to (a) in meters, and your answer to (b) as a positive (counterclockwise) or negative (clockwise) angle of magnitude less than 180° from the original direction of motion.

Explanation / Answer

here,

let the car is initially at the origin

the displacement vector of the car , d

d = 1666.8 m j + 1000 m i - 60 m j + 777.78 i - 666.67 m j + 333.33 m i

d = 2111.11 m i + 940.13 j

(a)

the distance of the starting point , d = sqrt(2111.1^2 + 940.13^2)

d = 2310.97 m

the distance of the starting point is 2.31 km

(b)

theta = arctan(940.13/2111.1)

theta = 24 degree

the direction from thye initial point is 24 degree counter clockwise

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