Question

Objects of mass 2kg and 1 kg are moving along the same line and direction with velocities of 5 m/s and 10 m/s

respectively. They collide and after the collision the first object moves with the velocity of 7.2m/s.

Determine the velocity of the second object​

Answer 1

Provided that:

• Mass of object one = 2 kg

• Mass of second object = 1 kg

• Object one's initial velocity = 5 mps

• Object second's initial velocity = 10 mps

• Final velocity of object one = 7.2 mps

To calculate:

• Final velocity of second object

Solution:

• Final velocity of second object = 5.6 mps

Using concept:

• Law of conservation of momentum

Using formula:

${\small{\underline{\boxed{\sf{\rightarrow \: m_A u_A + m_B u_B \: = m_A v_A + m_B v_B}}}}}$

(Where, ${\sf{m_A}}$ denotes mass of object one, ${\sf{u_A}}$ denotes initial velocity of object one, ${\sf{m_B}}$ denotes mass of object two, ${\sf{u_B}}$ denotes initial velocity of object two, ${\sf{v_A}}$ denotes final velocity of object one, ${\sf{v_B}}$ denotes final velocity of object two.)

Required solution:

$:\implies \sf m_A u_A + m_B u_B \: = m_A v_A + m_B v_B \\ \\ :\implies \sf 2(5) + 1(10) = 2(7.2) + 1(v_B) \\ \\ :\implies \sf 10 + 10 = 14.4 + v_B \\ \\ :\implies \sf 20 = 14.4 + v_B \\ \\ :\implies \sf 20 - 14.4 \: = v_B \\ \\ :\implies \sf v_B \: = 5.6 \: ms^{-1}$