Question

a 20 foot ladder leaning up against a vertical wall begins to slip. the base of the ladder makes an acute angle with the floor. when the angle equals 60 degrees the angle is decreasing at 0.1 radians/second. find the rate at which the height of th upper end of the ladder is changing when the angle equals 60 dregrees

Answer 1

a = angle to floor = 60 at t
h = height = 20 sin a

dh/dt = 20 cos a da/dt

at a = 60 deg, cos a = 1/2 and da/dt=-.1

dh/dt = 20 (1/2) (-.1)

= -1 ft/s