A particle is kept at rest at the origin. Another particle starts from 5 m , 0 , with a velocity of - 4 i ^ + 3 j ^ m s - 1 . Find their closest distance of approach.

As shown in the diagram, the particle P is at the origin, the particle Q is at 5 , 0 , and moving with - 4 i ^ + 3 j ^ . It means Q is moving, as shown in the figure. The direction of movement is, v → Q = - 4 i ^ + 3 j ^ tanθ = 3 4 ⇒ θ = 37 ° . To find the closest distance between P and Q , we shall draw a perpendicular line of motion Q . Length P R will be the closest distance of approach. From triangle P Q R , we can write, sin 37 ° = P R 5 ⇒ P R = 5 × 3 5 = 3 m This is the closest distance of approach.

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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

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 100

A ship is sailing towards the North, at a speed of

\sqrt{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.

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 101

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.

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 102

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?

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 103

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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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 104

A pipe that can rotate in a vertical plane is mounted on a cart. The cart moves uniformly along a horizontal path with speed ${\vec{v}}_{1} = 2 m s^{- 1}$ . At what angle $α$ to the horizontal should the pipe be placed, so that the raindrops falling vertically with velocity ${\vec{v}}_{2} = 6 m s^{- 1}$ , 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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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 105

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.

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 106

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.

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 107

A particle is kept at rest at the origin. Another particle starts from

(5 m, 0)

, with a velocity of

- 4 \hat{i} + 3 \hat{j} m s^{- 1}

. Find their closest distance of approach.

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

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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?