A bullet of mass 10 g is horizontally fired with velocity 300 m s⁻¹ from a pistol of mass 1 kg. What is the recoil velocity of the pistol?
- A.0.3 m s⁻¹
- B.3 m s⁻¹
- C.-3 m s⁻¹
- D.-0.3 m s⁻¹
Correct answer
Explanation
The correct answer is C, -3 m s⁻¹. By the conservation of momentum, the pistol moves back with 3 m s⁻¹, and the minus sign shows it moves opposite to the bullet.
Before firing, the pistol and bullet are at rest, so their total momentum is zero. After firing it must still be zero: m₁v₁ + m₂v₂ = 0. The bullet's momentum is 0.01 kg × 300 m s⁻¹ = 3 kg m s⁻¹. So the pistol's momentum is -3 kg m s⁻¹, and its velocity is -3 ÷ 1 = -3 m s⁻¹. This backward kick is the recoil that a shooter feels on the shoulder or hand.
A is wrong: 0.3 m s⁻¹ comes from forgetting to convert 10 g into 0.01 kg correctly, and it also misses the direction. B is wrong: 3 m s⁻¹ has the right size but no minus sign, so it suggests the pistol moves with the bullet. D is wrong: -0.3 m s⁻¹ has the right direction but a value ten times too small.
Exam tip: Recoil velocity = -(mass of bullet × velocity of bullet) ÷ mass of gun; always convert grams into kilograms first.
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