Question
A train moving at a constant speed of 68.0 km/h moves east for 33.0 min, then in a direction 40.0° east of due north for 30.0 min, and then west for 59.0 min. What is the average velocity of the train during this run?
Magnitude
km/h
Direction
° (counterclockwise east)
Magnitude
km/h
Direction
° (counterclockwise east)
Answers
East motion
x = 68 *33/60 * 68 sin 40 *30/60 - 68 *59/60
= 68* -.112 = -7.61 km east
North motion
68 * cos 40 * 33/60 = 28.7 km north
tan angle west of north = 7.61/28.7
so
angle west of north = 14.9
angle from East = 90 + 14.9 = 104.9
x = 68 *33/60 * 68 sin 40 *30/60 - 68 *59/60
= 68* -.112 = -7.61 km east
North motion
68 * cos 40 * 33/60 = 28.7 km north
tan angle west of north = 7.61/28.7
so
angle west of north = 14.9
angle from East = 90 + 14.9 = 104.9