Hunter's Recoil Speed Calculation
What is the recoil speed of the hunter?
A 60 kg hunter, standing on frictionless ice, shoots a 42 g bullet horizontally at a speed of 660 m/s. What is the recoil speed of the hunter? Express your answer with the appropriate units.
Recoil Speed Calculation
The recoil speed of the hunter can be found using 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, assuming no external forces are acting.
In this case, the hunter and the bullet are initially at rest, so the total momentum before the bullet is fired is zero. After the bullet is fired, the bullet moves horizontally with a certain momentum, and the hunter will move in the opposite direction with an equal and opposite momentum.
The momentum of an object can be calculated by multiplying its mass by its velocity. So, the momentum of the bullet can be found by multiplying its mass (42 g or 0.042 kg) by its velocity (660 m/s). The momentum of the hunter can be found by multiplying the hunter's mass (60 kg) by the unknown recoil velocity (V).
To find the recoil velocity, we equate the momentum of the bullet to the momentum of the hunter:
(0.042 kg) * (660 m/s) = (60 kg) * (-V)
Simplifying the equation, we get:
0.042 * 660 = 60 * (-V)
V = - (0.042 * 660) / 60
V = - 0.462 m/s
The negative sign indicates that the hunter moves in the opposite direction to the bullet. Therefore, the recoil speed of the hunter is 0.462 m/s in the direction opposite to the bullet.
Explanation
When a hunter standing on frictionless ice shoots a bullet horizontally, the conservation of momentum principle can be used to determine the recoil speed of the hunter. In this scenario, the initial momentum of the system is zero, as both the hunter and the bullet are at rest.
After the bullet is fired, it gains momentum in the forward direction while the hunter gains momentum in the backward direction to maintain the overall momentum of the system at zero. This leads to the calculation of the recoil speed of the hunter.
The recoil speed is calculated by equating the momentum of the bullet to the momentum of the hunter. By solving the equation, we find that the recoil speed of the hunter is 0.462 m/s in the direction opposite to the bullet.
Understanding the concept of momentum and its conservation in such scenarios helps in determining the motion of objects in response to external forces like firing a bullet. It showcases the fundamental principles of physics at play in everyday actions.