Benjamin C. answered • 03/05/23
Experienced College Math and Physics Tutor
Hello!
With related rates problems, you always have to start with a formula that can describe the result you are looking for, and then you can take the time derivative to hopefully have an equation that you can solve and plug in. In this case, you know the length of the ladder, the instantaneous velocity as it moves away from the wall, and the position of the ladder. It's asking for the rate of change of the angle between the floor and the ladder, so first ask: what formula relates what I already know with that angle. (Hint: use trigonometry). Then, in this case, you will probably want to take the implicit derivative and solve for dθ/dt, then you can plug in x, dx/dt, and you may have to calculate θ from the initial condition.
Hope this was helpful! Let me know if you need any more help.
Benjamin C.
Unfortunately I cant just show you the solution because that would be considered cheating, but I can tell you the equations you could start with. Here are your given variables: L = 10 ft, x = 6 ft, dx/dt = 1.2 ft/s. Now we have to come up with a formula that relates angle and position. We can use the SOH-CAH-TOA acronym to find a good trig function to use, and since we already have the adjacent side, we will use cosine. Cosine = adjacent / hypotenuse. Therefore cosθ = x / 10. From there you can take the time derivative and solve for dθ/dt03/05/23
Mahnoor S.
Can you show me the problem solved with steps03/05/23