A particle is projected with velocity  at such an angle that it just clears two walls of equal height h which are at a distance 2h from each other. Show that time of passing between the two walls is  from Physics Motion in A Plane Class 11 Manipur Board
Zigya Logo

Chapter Chosen

Motion in A Plane

Book Chosen

Physics Part I

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12

A particle is projected with velocity 2 square root of gh at such an angle that it just clears two walls of equal height h which are at a distance 2h from each other. Show that time of passing between the two walls is 2 square root of straight h over straight g end root.


Given, 

Velocity with which the particle is projected = 2square root of gh 

Height of the wall = h

Distance between the walls = 2h

Let the particle be projected at angle θ.

Time taken by particle to cross the two walls each of height 'h' is equal to difference of instants when it would be at a height h above ground.

The kinematics of motion of particle in vertical direction is given by, 

space space space space space space straight y space equals space straight y subscript straight o space plus space straight u subscript straight y straight t space plus space 1 half straight a subscript straight y straight t squared space
rightwards double arrow space straight h space equals space 0 space plus space straight u space sinθt space minus space 1 half gt squared space
rightwards double arrow space gt squared space minus space 2 usinθ space straight t space plus space 2 straight h space equals space 0

The space difference space of space the space instant space when space the space particle space is space at space height space straight h space is comma space

increment straight t space equals space fraction numerator square root of 4 straight u squared sin squared straight theta minus 8 gh end root over denominator straight g end fraction space space space space space space space

Here comma space straight u space equals space 2 square root of gh space

therefore space increment straight t space equals space fraction numerator square root of 16 ghsin squared straight theta space minus space 8 gh end root over denominator straight g end fraction space space space space... left parenthesis 1 right parenthesis

The space distance space travelled space by space particle space in space horizontal space direction space in space the space interval space increment straight t space is comma space

straight u space cosθ increment straight t space equals space 2 straight h

straight i. straight e. comma space 2 square root of gh cosθ fraction numerator square root of 16 ghsin squared straight theta space minus space 8 gh end root over denominator straight g end fraction space equals space 2 straight h

rightwards double arrow space space space cosθ square root of 16 space sin squared straight theta minus 8 end root space equals space 1 space

rightwards double arrow space space left parenthesis 1 minus sin squared straight theta right parenthesis space left parenthesis 16 sin squared straight theta space minus space 8 right parenthesis space equals space 1

rightwards double arrow space space space 16 space sin to the power of 4 straight theta space minus space 24 space sin squared straight theta space plus space 9 space equals space 0 space

rightwards double arrow space space space space space space sin squared straight theta space equals space fraction numerator 24 plus-or-minus square root of 576 minus 576 end root over denominator 32 end fraction space equals space 3 over 4

Substituting space the space value space of space sin squared straight theta space in space equation space left parenthesis 1 right parenthesis comma space we space get

increment straight t space equals space fraction numerator square root of 12 space gh space minus space 8 gh end root over denominator straight g end fraction equals square root of fraction numerator 4 straight h over denominator straight g end fraction end root

That is, 2 space square root of straight h over straight g end root is the time of passing between the two walls. 



249 Views

What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors. 


814 Views

What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views

Give three examples of scalar quantities.

Mass, temperature and energy
769 Views

What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views

Give three examples of vector quantities.

Force, impulse and momentum.
865 Views