The kick experienced when firing a rifle can be explained by Newton\'s third law

Question

The kick experienced when firing a rifle can be explained by Newton's third law. A .22-caliber rifle has a mass M = 5.6 kg, and a bullet with a mass m = 3.0 g leaves the barrel of the gun at a velocity of 357 m/s. (a) If the bullet starts from rest and leaves the gun barrel after t = 0.010 s, what was the acceleration of the bullet, ab ? Assume the bullet's acceleration is constant while it travels along the barrel.
ab = m/s2

(b) What was the force on the bullet? (Enter the magnitude only.)
N

(c) What was the magnitude of the force exerted on the gun?
N

(d) What acceleration, ar, did the gun experience? (Assume the bullet is traveling in the positive direction. Indicate the direction with the sign of your answer.)
ar = m/s2

(e) Compare the ratio of M and m to the ratio of the accelerations of each object.
M m =
ab ar = M = 5.6 kg, m = 3.0 g (a) If the bullet starts from rest and leaves the gun barrel after t = 0.010 s, what was the acceleration of the bullet, ab ? Assume the bullet's acceleration is constant while it travels along the barrel.
ab = m/s2

(b) What was the force on the bullet? (Enter the magnitude only.)
N

(c) What was the magnitude of the force exerted on the gun?
N

(d) What acceleration, ar, did the gun experience? (Assume the bullet is traveling in the positive direction. Indicate the direction with the sign of your answer.)
ar = m/s2

(e) Compare the ratio of M and m to the ratio of the accelerations of each object.
M m =
ab ar = t = 0.010 s, ab ab ar, ar M m ab ar M m

Explanation / Answer

a) ab = (v-u)/t = (357-0)/0.01 = 35700 m/s^2

b) F = m*a = 0.003*35700 = 107.1 N

c) same but oppiste direction, F = 107.1 N

d) ar = F/M = 107.1/5.6 = 19.125 m/s^2 (in the opposite direction)

e)

M/m = 5.6/0.003 = 1866.67


ab/ar = 35700/19.125 = 1866.67

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