Step-by-step explanation:
By Pythagoras theorem we know that
Hypotenuse² = Base² + Perpendicular²
h² = b² + p²
We have for ladder
h = 5 m
b = 3 m
5² = 3² + p²
p = 4 m
[tex]\frac{db}{dt}=0.4m/s\\\\\frac{dh}{dt}=0[/tex]
Differentiating h² = b² + p² with respect to time
[tex]2h\times \frac{dh}{dt}=2b\times \frac{db}{dt}+2p\times \frac{dp}{dt}\\\\5\times 0=3\times 0.4+4\times \frac{dp}{dt}\\\\\frac{dp}{dt}=-0.3m/s[/tex]
The top of the ladder is descending at 0.3 m/s.
