Question

An object 2.0 kg mass collides with another object 4.0 kg mass that moves at 11 m/s to the west, after the collision the first object moves at 4.0 m/s west and the second object moves at 12 m/s to the west.
What was the velocity of the first object before the collision?

Answer 1

Answer on Question 62444, Physics, Mechanics | Relativity

Question:

An object $2.0 \, kg$ mass collides with another object $4.0 \, kg$ mass that moves at $11 \, ms^{-1}$ to the west, after the collision the first object moves at $4 \, ms^{-1}$ west and the second object moves at $12 \, ms^{-1}$ to the west. What was the velocity of the first object before the collision?

Solution:

Let's assume that the first object with mass of $2.0 \, kg$ moves to the east and collides with the second object with mass of $4.0 \, kg$ that moves at $11 \, ms^{-1}$ to the west. After the collision, the first object moves at $4 \, ms^{-1}$ to the west and the second object moves at $12 \, ms^{-1}$ to the west. Also, for convenience, we assume that the second object moves in the positive direction to the west. Then, we can apply the law of conservation of momentum:

$$- m _ {1} v _ {1 i} + m _ {2} v _ {2 i} = m _ {1} v _ {1 f} + m _ {2} v _ {2 f},$$

here, $m_{1}, m_{2}$ are the masses of the objects, $v_{1i}, v_{2i}$ are its velocities before collision and $v_{1f}, v_{2f}$ are its velocities after collision.

From this equation we can find the velocity of the first object before the collision:

$$v _ {1 i} = - \frac {m _ {1} v _ {1 f} + m _ {2} v _ {2 f} - m _ {2} v _ {2 i}}{m _ {1}}.$$

Let's substitute the numbers:

$$v _ {1 i} = - \frac {2 . 0 \, kg \cdot 4 \, ms ^ {- 1} + 4 . 0 \, kg \cdot 12 \, ms ^ {- 1} - 4 . 0 \, kg \cdot 11 \, ms ^ {- 1}}{2 . 0 \, kg} = - 6 \, ms ^ {- 1}.$$

The sign minus indicates that the velocity of the first object before the collision is directed to the east.

Answer:

$$v _ {1 i} = 6 \, ms ^ {- 1}.$$

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