A projectile is thrown with an initial velocity of v → = a i ^ + b j ^ . If the range of a projectile is double the maximum height reached by it. Find the ratio b a .

The horizontal range R of a projectile motion, R = u 2 sin 2 θ g = 2 u 2 sin θ cos θ g Maximum height H attained by the particle in projectile motion is H = u 2 sin 2 θ 2 g From the above expressions, H R = 1 4 sin θ cos θ ⇒ tan θ = 4 H R Given, Range of a projectile is double the maximum height of projectile. i.e., R H = 2 Thus, tan θ = 4 H R = 2 . . . i Also given, Initial velocity of projectile, v → = a i ^ + b j ^ The angle of projection, θ = tan - 1 ν y v x = tan - 1 b a or tanθ = b a . . . ii From the equations i and ii tan θ = b a = 2 . Therefore, the ratio b a = 2 .

A projectile is thrown with an initial velocity of v → = a i ^ + b j ^ . If the range of a projectile is double the maximum height reached by it. Find the ratio b a .

The horizontal range R of a projectile motion, R = u 2 sin 2 θ g = 2 u 2 sin θ cos θ g Maximum height H attained by the particle in projectile motion is H = u 2 sin 2 θ 2 g From the above expressions, H R = 1 4 sin θ cos θ ⇒ tan θ = 4 H R Given, Range of a projectile is double the maximum height of projectile. i.e., R H = 2 Thus, tan θ = 4 H R = 2 . . . i Also given, Initial velocity of projectile, v → = a i ^ + b j ^ The angle of projection, θ = tan - 1 ν y v x = tan - 1 b a or tanθ = b a . . . ii From the equations i and ii tan θ = b a = 2 . Therefore, the ratio b a = 2 .

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A projectile is thrown with an initial velocity of $\vec{v} = a \hat{i} + b \hat{j}$ . If the range of a projectile is double the maximum height reached by it. Find the ratio $\frac{b}{a}$ .

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>CONCEPT APPLICATION EXERCISE 5.2>Q 10

A ball is thrown at different angles with the same speed

u

and from the same points and it has the same range in both cases. If

y_{1}

and

y_{2}

be the heights attained in the two cases, then find the value of

y_{1} + y_{2}

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JEE Advanced

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 11

A particle $P$ is projected with the velocity $u_{1}$ at an angle of $30 °$ with the horizontal. Another particle $Q$ is thrown vertically upwards with velocity $u_{2}$ from a point vertically below the highest point of the path of $P$ . Determine the necessary condition for the two particles to collide at the highest point.

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 12

Two seconds after projection, a projectile is travelling in a direction inclined at

30 °

to horizontal. After one more second, it is travelling horizontally. Find the magnitude and direction of its velocity.

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 13

Two particles are separated at a horizontal distance $x$ as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. Find the time after which the horizontal distance between the particles becomes zero.

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 14

The horizontal range

(R)

of a projectile becomes

(R + 2 H)

from

R

due to wind in the horizontal direction. Here,

H

is the maximum height reached by the projectile. What constant horizontal acceleration is imparted by the wind.

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>CONCEPT APPLICATION EXERCISE 5.2>Q 15

A boy is running along the positive

x

-axis with

8 m s^{- 1}

. While running he manages to throw a stone in a plane perpendicular to his direction of running with the velocity

12 m s^{- 1}

at an angle

30 °

with vertical. Find the speed of the stone at the highest point of the trajectory.

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.22

A rubber ball escapes from the horizontal roof with a velocity $v = 5 m s^{- 1} .$ The roof is situated at a height, $h = 20 m$ . If the length of each car is equal to $x_{0} = 4 m$ , which car will the ball hit?

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PHYSICS For Joint Entrance Examination JEE (Advanced) Mechanics I>Chapter 5 - Kinematics II>ILLUSTRATION 5.23>Q (a)

(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?

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

A projectile is thrown with an initial velocity of v→=ai^+bj^. If the range of a projectile is double the maximum height reached by it. Find the ratio ba.

Important Questions on Kinematics II

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A projectile is thrown with an initial velocity of $\vec{v} = a \hat{i} + b \hat{j}$ . If the range of a projectile is double the maximum height reached by it. Find the ratio $\frac{b}{a}$ .