Rain is falling vertically downwards with a speed of 30 m/s. A man is running towards east with a speed of 10 m/s. At what angle with the vertical should he hold his umbrella to protect himself from the rain?

A boat takes 2 hours to travel 8 km and back in still water. If the velocity of the river is 4 km/h, the time taken by the boat to travel 8 km upstream and back is:

Two trains one of 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are $0.3\,\,m/{s^2}$ and $0.2\,\,m/{s^2}$  respectively, then the time taken to pass each other will be

A passenger train is running on a railways track with a speed ${v_1}$. While driving, the driver discovers that another goods train is travelling in front of the passenger train with a speed {v_2}\left( {{v_1} > {v_2}} \right). Its retardation after applying brakes is a. The least distance the passenger train must travel to avoid collision with goods train is

A 210 m long train is moving due North at a speed of 25 m/s. A small bird is flying due South a little above the train with speed 5 m/s. The time taken by the bird to cross the train is

A bird flies at 10 m/s due north while the wind blows at 5 m/s due east. What is the magnitude of the bird's velocity relative to the ground?

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is

Two cars A and B are moving with velocities $\vec{v_A} = 40\hat{i}$ km/h and $\vec{v_B} = -30\hat{j}$ km/h relative to the ground. A third car C is moving such that its velocity relative to car A is $\vec{v_{CA}} = 30\hat{j}$ km/h and relative to car B is $\vec{v_{CB}} = 40\hat{i}$ km/h. What is the speed of car C relative to the ground?

The jet airplane travelling at the speed of 500 km/h ejects its products of combustion at the speed of 1500 km/h, relative to the jet plane. The speed of the latter with respect to an observer on the ground is

Two trains 101 m and 99 m in length are running in opposite direction with velocities 54 km/h and 36 km/h. In what time they will completely cross each other ?

A bird files for 4s with a velocity of $\left| {t - 2} \right|{\rm{m}}{{\rm{s}}^{ - 1}}$ in a straight line, where t=time in second. It covers a distance of