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IMPORTANT
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A man is swimming in a lake in the direction of 30° East of North with a speed of 5 km h-1, and a cyclist is going on a road along the lakeshore towards the East at a speed of 10 km h-1. In what direction and with what speed would the man appear to swim to the cyclist?

Important Questions on Kinematics

EASY
JEE Main/Advance
IMPORTANT
A ship is sailing towards the North, at a speed of 2 m s-1. The current is taking it towards the East at the rate of 1 m s-1, and a sailor is climbing a vertical pole on the ship, at the rate of 1 m s-1. Find the velocity of the sailor with respect to the ground.
EASY
JEE Main/Advance
IMPORTANT
A swimmer's speed in the direction of the flow of a river is 16 km h-1. Swimmer's speed against the direction of flow of the river is 8 km h-1. Calculate the swimmer's speed in still water and the velocity of flow of the river.
MEDIUM
JEE Main/Advance
IMPORTANT
A man can swim with a speed of 4 km h-1 in still water. How long does he take to cross a river, which is 1 km wide, if the river flows steadily at 3 km h-1, and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
MEDIUM
JEE Main/Advance
IMPORTANT
A river is flowing from the West to the East, at a speed of 5 m min-1. A man on the South bank of the river, capable of swimming at 10 m min-1 in still water, swims across the shortest path distance. In what direction should he swim?
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JEE Main/Advance
IMPORTANT

A pipe that can rotate in a vertical plane is mounted on a cart. The cart moves uniformly along a horizontal path with speed v1=2 m s-1. At what angle α to the horizontal should the pipe be placed, so that the raindrops falling vertically with velocity v2=6 m s-1, move parallel to the axis of the pipe without touching its walls? Consider the velocity of the drops as constant due to the resistance of the air.

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MEDIUM
JEE Main/Advance
IMPORTANT
Rain seems to be falling vertically to a person sitting in a bus, which is moving uniformly Eastwards with 10 m s-1. It appears to come from the vertical, at a velocity of 20 m s-1. Find the speed of the raindrops with respect to the ground.
MEDIUM
JEE Main/Advance
IMPORTANT
Rain appears to fall vertically when a man walks at the rate of 2 km hr-1 with respect to the ground.  When he increases his speed to 4 km hr-1, in the same direction of his motion, rain appears to meet him at an angle of 45° with horizontal, find the real direction and the speed of the rain.
EASY
JEE Main/Advance
IMPORTANT
A particle is kept at rest at the origin. Another particle starts from 5 m, 0, with a velocity of -4i^+3j^ m s-1. Find their closest distance of approach.