Question

A car goes east for 12 minutes at a speed of 30 km per hour, then turns 30° north and proceeds for 30minutes at a speed of 45 km/hr Where is the car relative to its starting point at the end of this time. Please show all work with steps.

Answer 1

Initial distance covered = 30*12/60 = 6 Km

Then 30 degree north, distance covered = 45*30/60=22.5 Km

Now let us assign cartesian coordinates to these directions. Let initial direction be x and north be y. Then, initial distance in vector form will be 6 i Km. Also, Unit vector in 30 degrees north direction will be cos30 i + sin30 j = 0.866 i + 0.5 j. So second displacement in vector form will be 22.5(0.866 i + 0.5 j) .

Hence total displacement in vector form= (6 + 19.485) i + 11.25 j = 25.485 i + 11.25 j

, i.e,The car is 25.485 in the initial direction and 11.25 north of the starting point.