The problems involving relative velocity can be solved using the laws of vectors. In other words, the relative velocity problems are nothing but the vectors problems. The first step is to represent the velocities in the form of vector and finally using the vector addition, finding the missing variable.
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An example of a relative velocity problem and its answer with the solutionProblem: A Rocket is moving with the speed of 1500 km/hr. It ejects hot gases at a speed of 900 km/hr with respect to rocket. Find the speed of gases with respect to ground.Solution: Let the speed of Rocket be Vr and the speed of gases with respect to rocket is Vgr.
Let the positive direction be taken as the direction of movement of Rocket.Therefore,Vr = 1500 km/hrVg="?"Vgr="-900" km/hrNow,Vgr = Vg - VrVg = Vr + Vgr= 1500 - (900) = 600 km/hr.Therefore , the speed of hot air with respect to ground is 600 km/hr.Here are some of the relative velocity problems and their answers.
Relative Velocity Problems and Their Answers.Problem: A bus P is moving at a speed of 50 km/hr and another Bus Q moving at 30 km/hr in opposite direction. Find out the relative velocity of the Bus P with respect to the Bus Q.( Answer: 80 km/hr)Problem: A swimmer can swim is still water at a rate of 8.0 km/hr. If he swims in a river flowing at 6.0 km/hr and keeps his direction (with respect to water) perpendicular to the current, find his velocity with respect to ground. (Answer: 10.0 km/hr )Problem:
A man is walking on a level road at a speed of 6.0km/hr. Raindrops fall vertically with a speed of 8.0 km/hr. Find the velocity of the raindrops with respect to man. (Answer: 10.0 km/hr).Problem: A girl moves with a velocity of (0.6i - 2j ) m/sec. She receives rains at a velocity (0.4 i- 2j) m/sec. Find the speed of raindrops with respect to ground. (Answer:`sqrt(17)`