A marksman at rest fires a 4.00-kg gun that expels a bullet of mass 0.0140 kg with a velocity of 181 m/s. The marksman's mass is 81.0 kg. What is the marksman's velocity after firing the gun?
mc = 85kg
md = 0.0140
-(0.0140)(-181)/85
= .0298 m/s
Thanks for nothing Bob
To calculate the marksman's velocity after firing the gun, we can use the principle of conservation of momentum. The total momentum before firing should be equal to the total momentum after firing.
The initial momentum of the marksman and the gun is given by:
Initial momentum = mass_marksman x velocity_marksman = 81 kg x 0 m/s = 0 kg*m/s
The momentum of the bullet after being fired can be calculated as:
Momentum_bullet = mass_bullet x velocity_bullet = 0.0140 kg x 181 m/s = 2.534 kg*m/s
The final momentum after firing should be equal to the initial momentum, so:
Final momentum = Initial momentum + Momentum_bullet
Final momentum = 0 kg*m/s + 2.534 kg*m/s = 2.534 kg*m/s
To find the final velocity of the marksman, we divide the final momentum by the mass of the marksman:
Final velocity_marksman = Final momentum / mass_marksman = 2.534 kg*m/s / 81.0 kg = 0.0313 m/s
Therefore, the marksman's velocity after firing the gun is approximately 0.0313 m/s.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event.
Before firing the gun, both the marksman and the gun are at rest, so their initial momentum is zero.
After firing the gun, the gun recoils backward due to the forward momentum of the bullet. Let's assume the marksman's velocity after firing the gun is v.
The initial momentum before firing is equal to the final momentum after firing. Mathematically, we can express this as:
(0 kg) + (81 kg)(0 m/s) = (4.00 kg + 0.0140 kg) * v
Simplifying this equation, we get:
0 = 4.014 kg * v
Dividing both sides of the equation by 4.014 kg, we find:
v = 0 m/s
Therefore, the marksman's velocity after firing the gun is 0 m/s. This means that the marksman stays at rest after firing the gun.
Answered by BobPursley following a repost.
They apparently want you to assume the marksman and gun recoil backwards together, as a rigid body with no force keeping them in place. That isn't really what happens, although it does apply to the center of mass of gun and marksman for a brief instant.