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: 60 km/h for 3.0 min, turn 90° to the right, 20 km/h for 7.0 min, turn 90° to the right, 20 km/h for 60 s, turn 90° to the left, 50 km/h for 80 s, turn 90° to the right, 20 km/h for 1.0 min, turn 90° to the left, 50 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

Hi, Consider a x-y co-ordinate system and the first travel towards the +ve y-direction. Now if you can draw a free hand diagram it can be observed that all displacements are along x or y directions (+ve or -ve) as below: a) 60 km/h for 3.0 min => 16.667 m/s for 180sec = 3000.06m +ve y direction b) 20 km/h for 7.0 min => 5.556 m/s for 420sec = 2333.52m +ve x direction c) 20 km/h for 60 s => 5.556 m/s for 60sec = 333.36m -ve y direction d) 50 km/h for 80 s => 13.889 m/s for 80sec = 1111.12m +ve x direction e) 20 km/h for 1.0 min => 5.556 m/s for 60sec = 333.36m -ve y direction f) 50 km/h for 30 s => 13.889 m/s for 30sec = 416.67m +ve x direction. Hence the resultant x-displacement = x = 2333.52m + 1111.12m + 416.67m                                                     = 3861.31m     and the resultant y-displacement = y = 3000.06m - 333.36m - 333.36m                                                     = 2333.34m. And hence the resultant displacement from the initial position = sqrt(x^2 + y^2)                                                           = 4511.562m and making an angle arctan(y/x) = 31.14 deg with +ve x-axis counter-clockwise. Hope this helps you. Hope this helps you.

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