“A ball is thrown from the edge of a high cliff. Regardless of the angle at which it is thrown, due to air resistance, the ball will eventually end up moving vertically downward.” Justify this statement.

Solution 33DQ After the ball is thrown, there will be two force acting on the ball. 1. The gravitational force, which is vertically downward. 2. The air resistance, will always act against the velocity and is proportional to the velocity. There will be two component of the velocity, vertical and horizontal component. The horizontal component of the air resistance will decrease the horizontal velocity and will become zero at some time. When the horizontal component of the velocity will be zero, no horizontal component of the air resistance will also be zero and hence there will be no horizontal force. Hence the horizontal velocity will remain zero afterward. Now, during going up, both vertical component of air resistance and gravity will act in same direction and reduce the velocity and the velocity will become zero. When the velocity of the ball become zero, the air resistance becomes zero, but gravity will still act. So the ball will become accelerate downward. When the ball is now going down, the air resistance and gravity will act against each other. Now initially the gravity is higher than air resistance and hence the ball will accelerate downward. As the velocity increases, the air resistance increases, this will reduce the acceleration, but the ball will still accelerate and will go downward. Now if the height is sufficient, at certain point, the air resistance will be equal to the gravity and then the total force will be zero. So ball will not accelerate further, but it will continue moving downward with constant velocity. So we have seen that even though the horizontal component of velocity will become zero at certain point of time the vertical component will nver. Hence after certain point of time the ball will start moving downward.