During a nice afternoon in a large park, a student runs in the following pattern

Question

During a nice afternoon in a large park, a student runs in the following pattern: 3km east, 4 km south, 3 km east, and 12 km north. a) Sketch the vector displacements the students ran in the park. b) What is the resulting vector R vector for this run? Use standard unit vector notation as defined in class. c) What is the magnitude of the resulting vector R vector for the run? d) What is the angle of the resulting vector R vector from the East direction for the run? Remember to use the trigonometry table on the back page. e) Assume the student launches a weather balloon when he finishes the run at the point where resulting vectors was measured in Parts (a) to (d) above. This weather balloon reaches an altitude of 20 (2^0.5) km (28.28 km) above the ground before it pops. What is the distance from the runner's starting point to the position where the balloon popped? Assume the Earth surface is flat on the scale of this problem and there is no wind.

Explanation / Answer

taking strating position, x0 = (0, 0, 0)

displacement of runner = 3i - 4j + 3i + 12j

= 6i + 8j km

final position, xf = (6, 8, 0) km

position of ballon, xB = (6, 8, 28.28) km

displacement of balloon from strating position,

r = 6i + 8j + 28.28k

distance = sqrt(6^2 + 8^2 + 28.28^2)

= 30 km .........Ans

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