A hunter on a frozen, essentially frictionless pond uses a rifle that shoots 4.20 g bullets at 970 m/s . The mass of the hunter (including his gun) is 69.5 kg , and the hunter holds tight to the gun after firing it.
What kind of skccool subject is "umkc"?
And what is your question?
Sorry, typo: not skccool -- school!
To determine the speed at which the hunter will move backward after firing the rifle, we need to apply the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces are acting on it. In this case, the hunter and the bullet are considered as a closed system.
First, we need to find the momentum of the bullet. The momentum of an object can be calculated by multiplying its mass and its velocity.
Momentum (P) = mass (m) × velocity (v)
Given:
Mass of the bullet (m) = 4.20 g = 0.00420 kg
Velocity of the bullet (v) = 970 m/s
Momentum of the bullet = 0.00420 kg × 970 m/s = 4.074 kg·m/s
Since the hunter holds tight to the gun after firing, the total momentum of the closed system (hunter + bullet) before firing is zero.
Now, let's represent the mass of the hunter as "M" and the velocity at which the hunter moves backward as "V."
Using the principle of conservation of momentum, we can write the equation:
Total initial momentum = Total final momentum
(0 kg) + (69.5 kg)(0 m/s) = (69.5 kg + 0.00420 kg)(-V)
Simplifying the equation:
0 = (69.5 kg)(-V) + (0.00420 kg)(-V)
0 = -69.5V - 0.0042V
0 = -69.5042V
Solving for V:
V = 0
This means that the hunter will move backward with a velocity of 0 m/s after firing the rifle.