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.

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

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.

Important Questions on Kinematics

MEDIUM

JEE Main/Advance

IMPORTANT

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.

MEDIUM

JEE Main/Advance

IMPORTANT

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.

EASY

JEE Main/Advance

IMPORTANT

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.

MEDIUM

JEE Main/Advance

IMPORTANT

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.

EASY

JEE Main/Advance

IMPORTANT

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})

EASY

JEE Main/Advance

IMPORTANT

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)

MEDIUM

JEE Main/Advance

IMPORTANT

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

Question Image

EASY

JEE Main/Advance

IMPORTANT

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

Question Image

Important Questions on Kinematics

Learn and Prepare for any exam you want !