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Answer :
a. The recoil velocity of the 5.0 kg rifle is 2.0 m/s in the opposite direction of the bullet's velocity.
b. The recoil velocity of the 2.0 kg rifle is 0.5 m/s in the opposite direction of the bullet's velocity.
c. the recoil velocity of the 5.0 kg rifle is greater (2.0 m/s) than the recoil velocity of the 2.0 kg rifle (0.5 m/s).
a) To calculate the recoil velocity of a rifle, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.
The momentum of an object is given by the product of its mass and velocity. Let's denote the mass of the rifle as Mr, the mass of the bullet as Mb, the initial velocity of the bullet as Vb, and the recoil velocity of the rifle as Vr.
Before the bullet is fired, the rifle and the bullet are at rest, so their total momentum is zero. After the bullet is fired, the momentum of the rifle and the bullet must still add up to zero to conserve momentum.
The momentum of the bullet is given by Mb * Vb, and the momentum of the rifle is given by Mr * Vr. So we have the equation:
Mb * Vb + Mr * Vr = 0
We can rearrange this equation to solve for Vr:
Vr = -(Mb * Vb) / Mr
Plugging in the values given in part (a):
Mb = 0.020 kg
Vb = 100 m/s
Mr = 5.0 kg
Vr = -(0.020 kg * 100 m/s) / 5.0 kg
Vr = -2.0 m/s
The recoil velocity of the 5.0 kg rifle is 2.0 m/s in the opposite direction of the bullet's velocity.
b) Similarly, for part (b):
Mb = 0.010 kg
Vb = 100 m/s
Mr = 2.0 kg
Vr = -(0.010 kg * 100 m/s) / 2.0 kg
Vr = -0.5 m/s
The recoil velocity of the 2.0 kg rifle is 0.5 m/s in the opposite direction of the bullet's velocity.
c) To determine which rifle has a bigger recoil, we compare the absolute values of their recoil velocities.
In this case, the recoil velocity of the 5.0 kg rifle is greater (2.0 m/s) than the recoil velocity of the 2.0 kg rifle (0.5 m/s).
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