Answer:3.75 ft/s
Step-by-step explanation:
Given
Length of ladder(L)=40 feet
base of ladder moves at a rate of 5 ft/sec
Bottom of ladder from wall(x)=24 feet
let horizontal distance be x and vertical distance be y
![y=√(40^2-24^2)=32](https://img.qammunity.org/2020/formulas/physics/high-school/9fodutbeg7qje8gjdtn1x02i4r6gesyp8x.png)
therefore
from Pythagoras
differentiate
![2x* \frac{\mathrm{d} x}{\mathrm{d} t}+2y\frac{\mathrm{d} y}{\mathrm{d} t}=0](https://img.qammunity.org/2020/formulas/physics/high-school/jixxchnj3tcthukjkun85wm3gvrajx72lx.png)
![x* \frac{\mathrm{d} x}{\mathrm{d} t}=-y* \frac{\mathrm{d} y}{\mathrm{d} t}](https://img.qammunity.org/2020/formulas/physics/high-school/vmj9g9q096fbh2ns3rovg0t7i61sugh2r1.png)
![24* 5=-32* \frac{\mathrm{d} y}{\mathrm{d} t}](https://img.qammunity.org/2020/formulas/physics/high-school/apqfmj1elfa438qjad5nh8rxajp6vrqq7i.png)
![\frac{\mathrm{d} y}{\mathrm{d} t}=(-3)/(4)* 5=-3.75 ft/s](https://img.qammunity.org/2020/formulas/physics/high-school/48i4agl2i6ifj1gsvg3hl1nhqh10xh592h.png)
negative sign indicates height is decreasing