A man standing on very slick ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kg , and the mass of the bullet is 10 g
If the bullet leaves the muzzle at a speed of 500 m/s, what is the final speed of the man?
Conservation of momentum problem
since system is a rest before firing
0 = m1*v1 + m2*v2
everything is given in problem besides v1
So solve for v1
a formula if possible would be awesome
awesome thanks
-0.07
To determine the final speed of the man, we can apply the principle of conservation of momentum. According to this principle, the total momentum before a collision or an event is equal to the total momentum after the collision or event, assuming there are no external forces.
In this case, before the bullet is fired, the man and the rifle have a combined momentum of zero since they are initially at rest. After the bullet is fired horizontally, the bullet and the remaining system (man + rifle) will have a combined momentum.
To find the final speed of the man, we need to calculate the speed of the combined system (bullet + man + rifle) after the bullet is fired, and then subtract the contribution of the bullet's momentum from this total.
First, let's convert the mass of the bullet to kilograms: 10 grams = 0.01 kg.
The momentum of an object is given by the product of its mass and velocity, so we can calculate the momentum of the bullet:
Momentum of the bullet = mass of the bullet * velocity of the bullet
= 0.01 kg * 500 m/s
= 5 kg·m/s
Now, to find the final speed of the man, we need to determine the momenta of the combined system before and after the bullet is fired.
Before the bullet is fired, the man and the rifle have a combined momentum of zero, so we can write this equation:
Momentum before = Momentum after
0 = (mass of the man + mass of the rifle) * final speed of the man
Now, let's plug in the values we know into this equation:
0 = (70 kg + mass of the rifle) * final speed of the man
To isolate the final speed of the man, we need to find the mass of the rifle. Since it is not given in the question, let's assume a mass value for the rifle. For example, if we assume the rifle has a mass of 5 kg, we can solve for the final speed of the man:
0 = (70 kg + 5 kg) * final speed of the man
0 = 75 kg * final speed of the man
final speed of the man = 0 m/s
Therefore, assuming a rifle mass of 5 kg, the final speed of the man after firing the bullet would be 0 m/s. However, keep in mind that this is an example calculation, and the actual mass of the rifle may vary.