A man is sitting in an open car which is travelling along a road at a speed of 30 m s - 1 . The man stands up and throws a ball at a speed of 15 m s - 1 relative to himself at an angle θ to the horizontal. The moment the man throws the ball, the driver of the car begins to accelerate at a constant rate of 10 3 m s - 2 , in the direction in which it was initially travelling. (a) Find the value of θ if the man in the car catches the ball. (b) Find the time at which the man catches the ball if the instant at which the ball was thrown is t = 0 . Assume that the time at which the ball travels contains the line of the motion of the car and that g = 10 m s - 2 .

You can attempt the problem in a reference frame fixed to the car or in the reference frame fixed to the ground. Fundamentally, these two reference frames are equivalent in all respects, but in the reference frame fixed to the car, the calculations are slightly easier. (a) Analysis of the motion of the ball in the reference frame fixed to the car: Let x -axis of the coordinate system be along the motion of the car and y -axis along the vertical direction. Acceleration of the ball in the reference frame, a → BR = Acceleration of the ball with respect to ground - Acceleration of the reference frame with respect to ground a → BR = ( - g j ^ ) - ( a i ^ ) = - a i ^ - g j ^ ⇒ a BR x = - a and a BR y = - g Let u be the velocity of the ball at t = 0 . Then u x = u cosθ and u v = u sinθ Using the equation, s = u t + 1 2 a t 2 in both x - and y -directions. Along x -direction: 0 = u cosθ t + 1 2 - a t 2 … ( 1 ) At t = t , x = 0 , y = 0 and 0 = u sinθ t + 1 2 - g t 2 … ( 2 ) The man catches the ball. From these equations, either t = 0 which refers to the initial condition or t = 2 u sinθ g from ( 2 ) and t = 2 u cosθ a from ( 1 ) 2 u sinθ g = 2 u cosθ a tanθ = g a = 10 10 3 = 1 3 . ⇒ θ = 30 ° b Time after releasing the ball at which man catches the ball again is given as t = 2 u sinθ g = 2 × 15 × 1 2 10 = 1 . 5 s

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(a) With what velocity $(v_{0})$ should a ball be projected horizontally from the top of a tower so that the horizontal distance on the ground is $η H$ , where $H$ is the height of the tower?

(b) Also determine the speed of the ball when it reaches the ground.

Important Questions on Kinematics II

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.24>Q (a)

A relief food package is dropped from a airplane which is moving horizontal with a velocity of $30 m s^{- 1}$ at a height $h =$ $50 m$ . Find the (a) time of flight of the package, (b) location of the point of striking of the food package, (c) velocity of the package at the time of striking the ground and (d) displacement of the food package.

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.25>Q (a)

A ball is thrown from the top of a building

45 m

high with a speed

20 m s^{- 1}

above the horizontal at an angle of

30 °

. Find
(a) The time taken by the ball to reach the ground.
(b) The speed of ball just before it touches the ground.

EASY

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.26

A boy travelling in an open car moving on a levelled road with constant speed tosses a ball vertically up in the air and catches it back. Sketch the motion of the ball as observed by a boy standing on the footpath. Give explanation to support your diagram.

EASY

JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.27

A boy throws a ball in air at

60 °

to the horizontal along a road with a speed of

10 {m s}^{- 1}

. Another boy sitting in a passing car observes the ball. Sketch the motion of the ball as observed by the boy in the car, if the car has a speed of

5 {m s}^{- 1}

. Give explanation to support your diagram.

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.28>Q (a)

A boy of height

1.5 m

, making move on a skateboard due east with velocity

4 m s^{- 1}

, throws a coin vertically up with a velocity of

3 m s^{- 1}

relative to himself.
(a) Find the total displacement of the coin relative to the ground till it comes to the hand of the boy.
(b) What is the maximum height attained by the coin w.r.t to ground?

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.29>Q (a)

A shell is projected from a gun with a muzzle velocity, $u$ . The gun is fitted with a trolley car at an angle $θ$ as shown in the figure. If the trolley car is made to move with constant velocity $y$ towards right, find the
(a) horizontal range of the shell relative to ground.
(b) horizontal range of the shell relative to a person travelling with trolley.

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.30>Q (a)

A man is standing on a rail road car travelling with a constant speed of $v = 10 {m s}^{- 1}$ (figure). He wishes to throw a ball through a stationary hoop $5 m$ above the height of his hands in such a manner that the ball will move horizontally as it passes through the hoop. He throws the ball with a speed of $12.5 {m s}^{- 1}$ with respect to himself.

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(a) What must be the vertical component of the initial velocity of the ball?
(b) How many seconds after he releases the ball will it pass through the hoop?
(c) At what horizontal distance in front of the loop must he release the ball?

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JEE Advanced

IMPORTANT

PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.31>Q (a)

A man is sitting in an open car which is travelling along a road at a speed of $30 m s^{- 1}$ . The man stands up and throws a ball at a speed of $15 m s^{- 1}$ relative to himself at an angle $θ$ to the horizontal. The moment the man throws the ball, the driver of the car begins to accelerate at a constant rate of $10 \sqrt{3} m s^{- 2}$ , in the direction in which it was initially travelling.
(a) Find the value of $θ$ if the man in the car catches the ball.
(b) Find the time at which the man catches the ball if the instant at which the ball was thrown is $t = 0$ .

Assume that the time at which the ball travels contains the line of the motion of the car and that $g = 10 m s^{- 2}$ .

(a) With what velocity v0 should a ball be projected horizontally from the top of a tower so that the horizontal distance on the ground is ηH, where H is the height of the tower? (b) Also determine the speed of the ball when it reaches the ground.

Important Questions on Kinematics II

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(a) With what velocity $(v_{0})$ should a ball be projected horizontally from the top of a tower so that the horizontal distance on the ground is $η H$ , where $H$ is the height of the tower?

(b) Also determine the speed of the ball when it reaches the ground.