Question

23. A particle is projected at 60° to the horizontal with a kinetic
energy K. The kinetic energy at the highest point is
a. zero
b.k/4
c.k/2
d. k
​

Answer 1

Answer:

Given:

Particle is thrown at 60° with the horizontal from the ground with Kinetic energy of K.

To find:

Kinetic energy at highest point.

Concept:

We can always imagine the projectile motion to be consisting of two simultaneously occurring linear motions : one in the x-axis and other in the y-axis.

We also know that gravitational acceleration acts on the projectile only in the Y direction and hence we get to see zero Y velocity know y component velocity at the highest point.

At the highest point we only see the horizontal component of velocity which is equal to the horizontal component of initial velocity at the time of projection because there is no involvement of acceleration along the x axis.

Calculation:

Let initial velocity be u and kinetic energy is K, we know K = ½mu².

Velocity at highest point will be u cos(θ)

So final Kinetic energy :

$KE2 = \dfrac{1}{2} m { \{ u \cos(60 \degree) \} }^{2}$

$= > KE2 = \dfrac{1}{2} m {u}^{2} \times {( \dfrac{1}{2} )}^{2}$

$= > KE2 = K \times {( \dfrac{1}{2} )}^{2}$

$= > KE2 = \dfrac{K}{4}$

So final answer :

$\boxed{ \red{ \huge{ \bold{KE2 = \dfrac{K}{4} }}}}$

Answer 2

AnswEr :

Option (B) is correct

We have to find the Kinetic Energy of the particle at highest point

Now,

Kinetic Energy of the particle is given as :

$\bullet \ \large{\underline{\boxed{\sf K = \dfrac{1}{2}Mv^2}}}$

Also,

Velocity of a particle along x axis is v cos ∅

When the object is projected with an angle 60° with the horizontal,the initial velocity of the particle becomes v.cos(60)

New Kinetic Energy of the object would be :

$\sf \: K' = \dfrac{1}{2} M(v.cos60) {}^{2} \\ \\ \longrightarrow \: \sf \: K' = \dfrac{1}{2} Mv {}^{2} \times \bigg(\dfrac{1}{2} \bigg) {}^{2} \\ \\ \longrightarrow \: \boxed{ \boxed{ \sf \: K' = \dfrac{K}{4}}}$

The Kinetic Energy of the particle at the highest point is 1/4 times of the Initial Kinetic Energy