A boat crossing a river moves with a speed of 3 m/s relative to the water. The water in the river has a uniform speed of 4 m/s due east relative to the Earth. The river is 120 m wide. If the boat heads due north (a) how long does the crossing take? (b) Calculate magnitude and direction of the velocity of the boat with respect to the Earth

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Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.