Question
A 20m ladder is leaning against a wall. Top of ladder is sliding down at 3m per second and the bottom is sliding away from the wall at 4m per second. How high is the top of the ladder and far is the bottom of the ladder from the wall.
Answers
Scott
h = height up wall
d = distance from wall
by Pythagoras... h² + d² = 20²
differentiating
... 2 h dh/dt + 2 d dd/dt = 0
substituting
... (2 * h * -3) + (2 * d * 4) = 0
... 8 d = 6 h ... d = ¾ h
h² + (¾ h)² = 400
solve for h
substitute back to find d
d = distance from wall
by Pythagoras... h² + d² = 20²
differentiating
... 2 h dh/dt + 2 d dd/dt = 0
substituting
... (2 * h * -3) + (2 * d * 4) = 0
... 8 d = 6 h ... d = ¾ h
h² + (¾ h)² = 400
solve for h
substitute back to find d
Erica
Thanks, Scott! I got the height as 16 and distance as 12m.