A truck is travelling due north descending a hill of slope angle `theta = tan^(–1) (0.1)` at a constant speed of `90 km//hr`. At the base of the hill there is a gentle curve and beyond that the road is level and heads `30^(@)` east of north. A south bound police car is travelling at `80 km//hr` along the level road at the base of the hill approaching the truck. Find the velocity of the truck relative to police car in terms of unit vectors `hati,hatj` and `hatk` . Take x axis towards east, y axis towards north and z axis vertically upwards.

Answer

`(40 hati + 158.9 hatj - 8.9 hatk) km hr^(-1)`