A rifle of mass 4.0\text{ kg} fires a bullet of mass 0.01\text{ kg} with a velocity of 400… — JAMB UTME

A rifle of mass $4.0\text{ kg}$ fires a bullet of mass $0.01\text{ kg}$ with a velocity of $400\text{ m s}^{-1}$ . What is the recoil velocity of the rifle?

$-1.0\text{ m s}^{-1}$ Answer
B
$1.0\text{ m s}^{-1}$
C
$-100\text{ m s}^{-1}$
D
$4.0\text{ m s}^{-1}$

Answer

The recoil velocity of the rifle is

-1.0\text{ m s}^{-1}

(or

1.0\text{ m s}^{-1}

in the direction opposite to the bullet).

The system starts at rest, so the initial total momentum is zero. By the law of conservation of linear momentum, the total final momentum must also be zero:

m_{rifle}v_{rifle} + m_{bullet}v_{bullet} = 0

. Substituting

m_{rifle} = 4.0\text{ kg}

m_{bullet} = 0.01\text{ kg}

, and

v_{bullet} = 400\text{ m s}^{-1}

gives

4.0 v_{rifle} + 4.0 = 0

, which yields

v_{rifle} = -1.0\text{ m s}^{-1}

. The negative sign indicates that the rifle moves in the direction opposite to the bullet.

Step-by-Step Solution

State the principle of conservation of linear momentum

Total Initial Momentum = Total Final Momentum = 0

Before firing, both the rifle and bullet are at rest.

Set up the linear momentum conservation equation

m_{rifle} v_{rifle} + m_{bullet} v_{bullet} = 0

The sum of the final momenta of the system components must equal zero.

Substitute the given numerical values into the equation and solve for recoil velocity

4.0 \cdot v_{rifle} + (0.01 \cdot 400) = 0 \implies 4.0 \cdot v_{rifle} + 4 = 0 \implies v_{rifle} = -1.0\text{ m s}^{-1}

Solving the linear algebraic equation yields the exact magnitude and direction of the recoil velocity.

Key Concept

Law of Conservation of Linear Momentum and Newton's Third Law of Motion

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic