A bullet of mass 0.45kg is fired from a gun of mass 9kg.the bullet moving with an initial velocity of 200m/s.find the intial backward velocity of the gun
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How to solve it
To find the initial backward velocity of the gun when a bullet is fired, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after an event remains constant.
Momentum (p) is calculated by multiplying an object's mass (m) by its velocity (v).
Initial momentum of the bullet + initial momentum of the gun = final momentum
The initial momentum of the bullet can be calculated as follows:
Mass of bullet (m1) = 0.45 kg
Initial velocity of bullet (v1) = 200 m/s
Momentum of bullet (p1) = m1 * v1
The initial momentum of the gun can be calculated as follows:
Mass of gun (m2) = 9 kg
Since the gun is initially at rest, the initial velocity of the gun (v2) is 0 m/s.
Momentum of gun (p2) = m2 * v2
Using the principle of conservation of momentum, we have:
p1 + p2 = p1' + p2'
Since the bullet is fired in one direction and the gun recoils in the opposite direction, the final velocity of the bullet is denoted as v1' and the final velocity of the gun is denoted as v2'.
Therefore, we can rewrite the equation as follows:
m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'
Since the initial velocity of the bullet, v1, is given as 200 m/s, and the mass of the bullet, m1, is given as 0.45 kg, we can substitute these values into the equation:
0.45 kg * 200 m/s + 9 kg * v2 = 0.45 kg * v1' + 9 kg * v2'
We are solving for the initial backward velocity of the gun, so v2' can be assumed to be zero since the gun comes to rest after being fired. This simplifies the equation to:
0.45 kg * 200 m/s + 9 kg * v2 = 0.45 kg * v1'
Simplifying further, we get:
90 kg m/s + 9 kg * v2 = 0.45 kg * v1'
Since the bullet comes to rest after being fired (v1' = 0 m/s), we can substitute this value into the equation:
90 kg m/s + 9 kg * v2 = 0
Solving for v2, we have:
9 kg * v2 = -90 kg m/s
v2 = -10 m/s
Therefore, the initial backward velocity of the gun is -10 m/s. The negative sign indicates that the gun recoils in the opposite direction to the bullet's motion.