How to Find the Height & Speed of Particles at Different Heights?

By Team Aakash Byju's | 12th January 2023

A particle is released from a height of H. At a certain height, its kinetic energy is two times its potential energy. The Height and speed of the particle at that instant are

C

A

B

D

H

3

,

4gH

3

2H

3

,

2gH

3

2H

3

,

2gH

H

3

,

2gH

√

√

√

√

Detailed Explanation

The correct answer is  A.

Arrow

H

3

,

4gH

3

√

The visual illustration of the given problem is shown below.

x

H

m

According to the law of conservation of energy, 'energy can neither be created nor be destroyed but it can be converted from one form to another.

The total energy (TE) of the ball of mass m at height H is

TE = mgH where, g is the gravity

Now, at a certain height h, TE will be converted to kinetic (KE) and potential (PE) energy such that KE = 2(PE)

=> TE = 2(PE) + PE = 3(PE) => mgH = 3(mgh)

=>  h =

H

3

Now, to find the velocity of the ball at height      , we use the formula of its kinetic energy.

KE =

H

3

1

2

mv

2

(    )

But, at height      , KE = 2(PE)

H

3

KE =

2mgH

3

mv

2

(    )

.  .

.

because

PE = mgh

= mg

H

3

K.E =

mgH

2

3

=

1

2

=>v  =

4

3

gH

2

v=

4

3

√

gH

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