Answer

Verified

385.8k+ views

**Hint:**A projectile stops at its highest point, so its vertical velocity becomes zero. It breaks into three individual systems. Since the system is isolated, the momentum and energy is conserved. Calculating velocity of each particle from the conditions and substituting corresponding values in the equation of law of conservation of momentum, we can calculate the missing velocity.

**Formula used:**

$mu={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}+{{m}_{3}}{{v}_{3}}$

**Complete step-by-step solution:**

The projectile breaks into three particles of masses- $m,\,m,\,2m$

Total mass of the projectile- $m+m+2m=4m$

At the highest point the vertical velocity becomes zero; therefore, the velocity of the projectile will be-

$v=u\cos \theta $, i.e. velocity in the horizontal direction.

As one particle traces back its path to the starting point, so its velocity will be-

$v'=-u\cos \theta $, negative sign indicates velocity is in the opposite direction.

One of the particles falls downwards vertically. So it will have pure vertical velocity and its horizontal velocity is 0.

As there are no external forces acting on the projectile, the system is conserved. This means that the initial momentum of the system is equal to the final momentum of the system. Therefore,

$\begin{align}

& mu={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}+{{m}_{3}}{{v}_{3}} \\

& \Rightarrow 4mu\cos \theta =-u\cos \theta +0+2mv'' \\

& \Rightarrow 5mu\cos \theta =2mv'' \\

& \Rightarrow 2v''=5mu\cos \theta \\

& \therefore v''=\dfrac{5}{2}u\cos \theta \\

\end{align}$

Therefore, the final velocity of the third particle of mass $2m$ is $\dfrac{5}{2}u\cos \theta $.

**Hence, the correct option is (D).**

**Note:**

When a system is isolated, it either travels with a constant velocity or remains at rest until an external force acts on it. In a projectile, a body has horizontal as well as vertical motion, so its velocity can be resolved in the horizontal component as well as the vertical component. In a projectile motion, a body follows a parabolic path.

Recently Updated Pages

Which of the following materials is likely to have class 8 physics CBSE

What is a quasar What is their importance class 8 physics CBSE

Identify the parts which vibrate to produce sound in class 8 physics CBSE

Write the relation between liter and cm3 class 8 physics CBSE

Define the terms a ray of light and a beam of ligh class 8 physics CBSE

Suppose you are in a car and it is raining heavily class 8 physics CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

Which are the Top 10 Largest Countries of the World?

The provincial president of the constituent assembly class 11 social science CBSE

Write the 6 fundamental rights of India and explain in detail