The distance from Patna to Ranchi is 260 km by air and 320 km by road. An aeroplane requires 30 minutes to travel from Patna to Ranchi, while a delux bus takes 8 hours. Determine the average velocity of the plane.

Step-by-step solution

Displacement of the aeroplane is the straight line distance between Patna and Ranchi, which is 260 km . Time taken by the aeroplane, t = 30 minutes = 1 2 h . Average velocity is defined as the ratio of displacement to time taken. Average velocity = Displacement t = 260 1 2 = 520 km/h . The direction of average velocity is along the displacement, which is from Patna to Ranchi.