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To cross the river in shortest distance, a swimmer should swim making angle θ with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance [assume speed of swimmer in still water is greater than the speed of river flow].

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Important Questions on Kinematics

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Raindrops are falling vertically with a velocity of 10 ms-1. To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of 20 ms-1. The velocity of cyclist is
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Two identical trains take 3 sec to pass one another when going in the opposite direction but only 2.5 sec if the speed of one is increased by 50% The time one would take to pass the other when going in the same direction at their original speed is:
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For four particles A, B, C and D the velocities of one with respect to the other are given as VDC is 20 m s-1 towards the north, VBC is 20 m s-1 towards the east and VBA is 20 m s-1 towards the south. Then VDA is
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A Person A observes B moving in east direction, with a speed 10 m s-1, B observes C moving in south direction, with a speed 20 m s-1, C observes D moving in west direction, with a speed 30 m s-1 and D  observes a tree, moving with speed 40 m s-1, in the north direction. The actual direction of motion of person A will be
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Three elephants A,B and C are moving along a straight line with constant speed in same direction as shown in figure. Speed of and speed of C is 10 ms-1. Initially separation between A & B is d and between B & C is also d. When B catches C separation between A & C becomes 3d. Then the speed of B will be 

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A particle A is at rest and particle B moves in a circle with A at it's centre. The particle A will appear
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An open elevator is ascending with zero acceleration and speed 10 ms-1. A ball is thrown vertically up by a boy when he is at a height 10 m from the ground, the velocity of projection is 30 ms-1 with respect to elevator. Choose incorrect option, assuming height of the boy very small g=10 ms-2.
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The block B is moving towards right with constant velocity v0. The velocity of block A with respect to block B is (assume all pulleys and strings are ideal),

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