CBSE Class 12-science Answered
The ladder, ground and wall form a right angled triangle with the ladder as the hypotenuse.
Let x = base length (foot of ladder to wall), let y=height (top of ladder to ground),
Then by Pythagoras, x2 + y2 = 172 ... (1)
The bottom of the ladder is being pulled, so these distances are changing with time.
Differentiating (1) with respect to time, using the chain rule, gives:
2x(dx/dt) + 2y(dy/dt) = 0 (2)
Rearranging (2), we get dy/dt = -x/y(dx/dt) (3)
From the question, x = 8 m, dx/dt = 5 m/s.
If x = 8 m, then from (1), y = 15 m
Putting these values into (3) we get dy/dt = -(8/15) x (5) = -8/3 m/s