Invincible Squirrels

How come a squirrel always survives a fall?

A squirrel can survive a fall from any height. This is a result of the drag force that comes from wind resistance. Let's look at how this works. A good approximation for the drag force is that it is proportional to the downward velocity of an object. Mathematically, F = -bv, where "b" is a constant and "v" is the velocity of the object. The other force acting on the squirrel is gravity. Mathematically, this is just F = mg. where "m" is the mass and "g" is a gravitational acceleration constant. Something to notice is that the force of gravity is constant. No matter how fast or slow an object is moving, the force of gravity near the surface of the earth is always the same. So how do the forces balance out? Initially, when the squirrel falls, it will have a velocity of 0 m/s. Since the drag force is proportional to the velocity, it is also 0 at this instant. The gravitational force will pull the squirrel towards the ground and it's velocity will begin to decrease. Because the velocity has increased, there is now an increased drag force that is pushing up on the squirrel away from the ground.

Figure 1

What begins to happen is that velocity of the squirrel continues to increase. As a result the drag force away from the Earth also increases, but the gravitational force towards the Earth stays constant. Eventually, the drag force will continue to increase until it reaches a point where it is equal to the gravitational force. At this instant, the forces will balance out so the speed of the squirrel will stop changing. Because the speed of the squirrel isn't changing, the drag force will now stay constant and equal to the force of gravity. This final speed that the squirrel reaches is called the terminal velocity. At this speed, the squirrel can survive the fall. The squirrel can always survive the fall because whether you drop it from the top of a tree or the top of the empire state building, the maximum speed it reaches is one it can survive.

Figure 2