A train travelling at a constant speed of 100 km/h travels west for 45 minutes, northwest for 30 minutes and finally north for 15 minutes. What is the trains average velocity for the trip?

Answer 1

Disp. = 100*(45/60)[180o] + 100*(30/60)[135o] + 100*(15/60)[90o].
Disp. = 100*0.75[180o] + 100*0.5[135] + 100*0.25[90o],
Disp. = -75 + 50[135] + 25[90o],
Disp. = (-75-50*Cos135) + (50*sin135+25)i = -110.4 + 60.4i = 126km[-28.7o] = 126km[28.7o N. of W.] = 126km[151.3o CCW).

V = Disp./t = 126km[151.3o]/(0.75+0.5+0.25) = 84km/h[151.3o].