A marksman at rest fires a potato gun that expels a potato of mass 0.512 kg with a velocity of 82.1 m/s. The marksman’s mass is 81.0 kg. What is the marksman’s velocity after firing the gun?
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To find the marksman's velocity after firing the gun, we can use the principle of conservation of momentum. According to this principle, the total momentum before firing the gun is equal to the total momentum after firing the gun.
The momentum of an object is calculated by multiplying its mass by its velocity. So, the momentum of the marksman before firing the gun is:
Marksman's momentum before = mass of marksman * velocity of marksman before firing
Given:
Mass of marksman (m1) = 81.0 kg
Velocity of marksman before firing (v1) = 0 m/s (at rest)
Therefore, the marksman's momentum before firing is 0 (since v1 is 0).
The momentum of the potato after being expelled from the gun is:
Potato's momentum after = mass of potato * velocity of potato
Given:
Mass of potato (m2) = 0.512 kg
Velocity of potato (v2) = 82.1 m/s
Therefore, the momentum of the potato after being expelled from the gun is:
Potato's momentum after = 0.512 kg * 82.1 m/s
Now, according to the conservation of momentum principle:
Total momentum before = Total momentum after
Since the marksman's momentum before is 0, we have:
0 = momentum of potato after
Therefore, to find the marksman's velocity after firing the gun, we need to rearrange the equation:
Marksman's momentum after = - (Potato's momentum after) [note: the negative sign indicates that the momentum of the marksman is in the opposite direction of the potato]
Now, we can calculate the marksman's velocity after firing the gun:
Marksman's momentum after = mass of marksman * velocity of marksman after firing
Therefore:
mass of marksman * velocity of marksman after firing = - (mass of potato * velocity of potato)
Solving for velocity of marksman after firing:
velocity of marksman after firing = - (mass of potato * velocity of potato) / mass of marksman
Substituting the given values:
velocity of marksman after firing = - (0.512 kg * 82.1 m/s) / 81.0 kg
Now we can calculate the marksman's velocity after firing the gun.