Explain how a parachutist's loss of momentum on landing is consistent with the principle of conservation of momentum?
The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act upon it. In the case of a parachutist landing, the loss of momentum is indeed consistent with this principle.
To explain why, let's consider the momentum of the parachutist before and after landing. Before landing, the parachutist is descending with a certain velocity. This velocity, along with the mass of the parachutist, determines their initial momentum. Let's call this momentum "p_initial".
When the parachutist lands, they come to a stop. This means their final velocity is zero. The momentum of the parachutist after landing, which we'll call "p_final", is therefore also zero, since momentum is calculated by multiplying an object's mass by its velocity.
According to the conservation of momentum, the total momentum of the system (parachutist + Earth) must remain constant. Because no external forces act on the parachutist during landing (ignoring air resistance for simplicity), the only forces involved are internal. In this case, it's the force exerted by the parachutist on Earth and vice versa.
Since the total momentum of the system must remain constant, the loss of momentum of the parachutist is balanced out by the gain of an equal momentum by the Earth. This means that the momentum lost by the parachutist during landing is transferred to the Earth, resulting in a total momentum of zero for both the parachutist and the Earth.
In simple terms, during landing, the parachutist exerts a force on the ground, and the ground exerts an equal and opposite force on the parachutist, leading to their loss of momentum. This transfer of momentum from the parachutist to the Earth is consistent with the principle of conservation of momentum.