Question

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1.1 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.)

Answer 1

 let: 
X = the distance of the bottom of the ladder from the wall at any time 
dX/dt = rate of travel of the bottom of the ladder = 1.1 ft/sec 
A = the angle of the ladder with the ground at anytime 
dA/dt = rate of change of the angle in radians per second 

X = 10 cos A 

dX/dt= -10 sin A dA/dt = 1.1 

dA/dt = -1.1/(10 sinA) 

When X = 6; cosA = 6/10; sinA = 8/10 

Therefore: 

dA/dt = -1.1/(10 x 0.8) = -0.1375 radiant per second.