Question

A 26 foot ladder is lowered down a vertical wall at a rate of 3 feet per minute. The base of the ladder is sliding away from the wall.

1. At what rate is the ladder sliding away from the wall when the base of the ladder is 10 feet from the wall?

Would you expect the same rate when the ladder is any distance from the wall?

Would you expect your answer to be positive when the base is any distance from the wall? Is there a physical reason why the rate is positive?

At what rate is the ladder moving away from the wall when the ladder hits the ground?

2. If you consider the triangle formed by the ladder, the wall, and the ground, at what rate is the area of the triangle changing when the base of the ladder is 10 feet from the wall?

What does the sign of your answer (whether it is positive or negative) say about the area of the triangle at that moment?

Would you expect the rate at which the area is changing to have the same sign (positive or negative) when the base of the ladder is any distance from the wall?

3. At what rate is the angle between the ladder and the ground changing when the base of the ladder is 10 feet from the wall?

Would expect the angle to be decreasing at a more rapid rate when the ladder is closer to a vertical position or a horizontal position?

Answer 1