Why must a water skier moving with constant velocity lean backward? What determines how far back she must lean?
drag (friction) from the ski/water interface would cause the skier to be pulled off the skis
... the backward lean exerts a forward force on the skis
the faster the skier goes, the greater the drag, and the more lean
A water skier moving with constant velocity must lean backward to maintain their balance and prevent themselves from falling forward. Leaning backward counteracts the forward force exerted on the skier by the movement of the boat. This is due to Newton's first law of motion, which states that an object in motion will stay in motion with the same velocity unless acted upon by an external force.
To understand why leaning backward is necessary, we need to consider the forces acting on the skier. When the boat accelerates forward, it creates a force that pushes the skier in the same direction. If the skier were to remain upright, without leaning backward, the force from the boat would cause their center of mass to move forward, causing them to lose balance and fall into the water.
By leaning backward, the skier shifts their center of mass slightly behind their feet, creating a torque or rotational force that opposes the forward force from the boat. This allows the skier to maintain their balance while being pulled by the boat.
The amount of backward lean required depends on various factors, including the speed of the boat, the angle of the skis, and the skier's weight distribution. Generally, the skier should lean back enough to counterbalance the forward force, but not excessively, as it could lead to loss of control or falling backward. Finding the right balance may require some trial and error, and experienced skiers develop a sense of how far back they need to lean based on their familiarity with their equipment and personal preferences.