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.

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 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.

Important Questions on Kinematics

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 108

Four particles, situated at the corners of a square of the side

a

, move at a constant speed

v

. Each particle maintains a direction towards the next particle in succession. Calculate the time the particles will take to meet each other.

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 109

An aero plane is flying vertically upwards with a uniform speed of

500 m s^{- 1}

. When it is at the height of

1000 m

above the ground, a shot is fired at it with a speed of

700 m s^{- 1}

from a point directly below it. The minimum uniform acceleration of the aero plane now so that it may escape from being hit?

(g = 10 m s^{- 2})

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 110

A stone is thrown upwards from a tower with a velocity

50 m s^{- 1}

. Another stone is simultaneously thrown downwards, from the same location with a velocity

50 m s^{- 1}

. When the first stone is at the highest point, the relative velocity of the second stone with respect to the first stone is (assume that the second stone has not yet reached the ground)

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 111

Shown in the figure, is the position-time graph for two children, going home from school. Which of the following statements about their relative motion is true, after both of them started moving? (Consider $1 - D$ motion). Their relative velocity

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 112

The figure shown below represents the velocity-time graphs of the two particles $P_{1}$ and $P_{2}$ moving along a straight line. The magnitude of their relative velocity

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 113

Two trains

A

and

B

, which are

100 km

apart, are travelling towards each other on different tracks with each having an initial speed of

50 km h^{- 1}

. The train

A

accelerates at

20 km h^{- 2}

and the train

B

retards at the rate of

20 km h^{- 2}

. The distance covered by train

A

when they cross each other is

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 114

A jet airplane traveling from east to west at a speed of

500 km h^{- 1}

ejects outgases of combustion at a speed of

1500 km h^{- 1}

with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?

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Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 115

A helicopter is flying south with a speed of

50 km h^{- 1}

. A train is moving at the same speed towards the east. The relative velocity of the helicopter as seen by the passengers in the train will be towards

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.

Important Questions on Kinematics

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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.