Question

A 10 kg object at rest explodes into four pieces. Each of the three pieces has a mass of 2.0 kg, and the
pieces travel due south, due east, and due west, respectively, at 3.0 m/s. What is the magnitude of the
velocity of the remaining piece?
(A) 1.0 m/s (B) 1.5 m/s (C) 3.0 m/s (D) 4.5 m/s

Answer 1

Given:-

Mass of object = 10kg

Mass of three Pieces = 2kg

Velocity of 3 Piece = 3.0m/s

To Find:-

The magnitude of the Velocity of the remaining Piece.

Formulae used:-

Conservation of Momentum

Now,

→ We know that the total mass if object is 10kg so and mass of 3 Pieces is 2kg so mass of 4th Piece would be (10 - 6) → 4kg.

Therefore,

Initially the Object was at rest.

So,

→ Total Momenta before exploding = Total Momenta after exploding.

→ 0 = m¹v¹ + m²v² + m³v³ + m⁴v⁴

→ 0 = ( m¹ + m² + m³ ) v + m⁴v⁴

→ 0 = ( 2 + 2 + 2)3 + m⁴v⁴

→ 0 = (6)3 + m⁴v⁴

→ 0 = 18 + m⁴v⁴

→ -18 = 4 × v⁴

→ v⁴ = -18/4

→ v⁴ = -4.5m/s

Hence, Option "D" is correct.

Answer 2

$\sf \underline{Given} :$

• A 10 kg object at rest explodes into four pieces.

• Each of the three pieces has a mass of 2.0 kg,

• the pieces travel due south, due east, and due west, respectively, at 3.0 m/s.

$\sf \underline{To \: Find} :$

• What is the magnitude of the velocity of the remaining piece?

$\sf \underline{Solution \: } :$

.

$\sf Mass \: of \: 4th \: piece \: is \: = 10 \: - 3 \times 2 \\ \\ \sf \: Mass \: of \: 4th \: piece \: is \: = 10 - 6 \\ \\ \sf \: Mass \: of \: 4th \: piece \: is \: =4$

Total Momenta before exploding

$\sf \mapsto 0 = m_1v_1 + m_2v_2+ m_3v_3+ m_4v_4 \\ \\ \\ </p><p></p><p> \sf \mapsto \: 0 = ( m_1 + m_2+ m_3 ) v + m_4v_4 \\ \\ \\ </p><p> \sf \mapsto \: 0 = ( 2 + 2 + 2)3 + m_4v_4 \\ \\ \\ </p><p></p><p> \sf \mapsto\: 0 = (6)3 + m_4v_4 \\ \\ \\ \sf \mapsto\: - 18 = 4 v_4 \\ \\ \\ \sf \mapsto\: v_4 = - \cancel{\frac{18}{4} } \\ \\ \\ \sf \mapsto\: v_4 = - \cancel{ \frac{9}{2} } \\ \\ \\ \sf \mapsto\: v_4 = -4.5$

Option d is correct