Duck Hunting: The Principle Of Conservation Of Momentum

Register to read the introduction… When I made my initial assessment of this situation, I realized that this collision can be described by the principle of conservation of momentum. Despite the somewhat imposing name, this principle is actually quite intuitive in nature. To understand this principle, I utilize an example from my own life: duck hunting. While some may consider it a rather barbaric pastime, I rather enjoy the thrill of venturing into a marsh in the early hours of the morning and I love the satisfaction of dressing and cooking a prize. You know immediately when your shot is a successful one; a bird flying in one direction is suddenly and violently launched in another direction falling precipitously. While the average pellet shot has a mass of no more than a few ounces and a duck weighs on the order of several pounds, the impact from the shot is enough to significantly redirect the trajectory of the duck. This occurs because while the pellet is very light, it is moving at an incredibly high speed relative to the duck. All moving massive objects possess this property of momentum, a quantity proportional to the mass of the object times its velocity. Momentum is what allows objects to exert forces; it is the mechanism whereby two objects in a collision can influence one another. When two objects collide, they both enter the collision with some momentum – both have some mass and some velocity – both leave with some momentum; however, the total momentum of the system before impact cannot exceed the total momentum of the system after impact. This is the principle of conservation of momentum. It is unreasonable to expect a duck struck by a pellet to fly off so fast it will escape the earth’s orbit, as it is unreasonable to expect nothing to …show more content…
By plugging in the values for v and θ, we get a value of 14.25 m/s for vx. A similar procedure is used to find the y-component of the velocity vector, which is given by: v ⃗_y=v ⃗ sin⁡θ (4)
Where vy represents the y component of the velocity vector in m/s, v is the velocity vector’s magnitude in m/s, and θ is the angle formed between the velocity vector v and the x-axis. Again, we plug in the appropriate values for v and θ, and we get a value of 8.23 m/s for vy. Armed with these values, we can move onto the last phase of this problem: application of the principle of conservation of momentum for inelastic collisions. In collisions where momentum is conserved, all individual component momenta are conserved independently. That is, the y-momentum conservation is not dependent on the x-momenta and vice versa. To make the math for this problem easier, we shall say that the north-south axis will be our y-axis and the east-west axis is our x-axis. For inelastic collisions – ones in which two bodies collide to become one with a common mass and velocity – the x and y momentum conservations are given by: m_1 v ⃗_x1i+m_2 v ⃗_x2i=(m_1+m_2)v ⃗_xf (5) m_1 v ⃗_y1i+m_2 v ⃗_y2i=(m_1+m_2)v ⃗_yf