Question

A bullet fired from gun with a velocity 30 m/s at an angle of 60° with horizontal direction. At the highest point of its path, the bullet explodes into two parts with masses in the ratio 1:3. The lighter mass comes to rest immediately. Then the speed of the heavier mass is

Options

• 30 m/s

• 20 m/s

• 10 m/s

• 5 m/s

Answer 1

20 m/s

Explanation:

Given `m_1/m_2 = 1/3`

∴ `(m_1 + m_2)/m_2 = (1 + 3)/3 = 4/3`

∴ `m/m_2 = 4/3`  ......(∵ m₁ + m₂ = m)

Now, mv = m₁v₁ + m₂v₂

Dividing by m₂, we get

`m/m_2 v = m_1/m_2 v_1 + m_2/m_2 v_2`

`4/3 v = 0 + v_2`  .....(∵ v₁ = 0)

At highest point, v = v cos θ

∴ `4/3 v cos theta` = v₂

i.e., v₂ = `4/3 xx 30 xx cos 60^circ = 4/3 xx 30 xx 1/2`

v₂ = 20 m/s