KFS Posted September 2, 2019 Share Posted September 2, 2019 In Example 1: I don't understand the procedure of this exercise. I do know why the derivative of the angle with respect to time is 2π/30. What I don't understand is the rest. It says x=10tanθ, how is this possible? It gives me, and the computer, by tanθ=opposite/adjacent, x=10/tanθ, not 10tanθ. What I don't understand either is why both derivatives (dx/dθ) and (dθ/dt) are multiplying. Why is x=8 choosen? Why not any other number? Thanks for the help. Link to comment Share on other sites More sharing options...
Ghideon Posted September 2, 2019 Share Posted September 2, 2019 (edited) 5 hours ago, KFS said: Why is x=8 choosen? Why not any other number? It looks like the problem could have been based on other number but author picked x=8. 5 hours ago, KFS said: It gives me, and the computer, by tanθ=opposite/adjacent, x=10/tanθ, not 10tanθ. Isn't θ is the angle at the lighthouse L between lines LQ and LP? Then x=8 is the opposite and 10 is the adjacent. tanθ=opposite/adjacent or tanθ=x/10 so x=10tanθ Hint regarding the derivatives: are you familiar with the chain rule for computing the derivative of the composition of two (or more) functions? Edited September 2, 2019 by Ghideon Added hint Link to comment Share on other sites More sharing options...
KFS Posted September 2, 2019 Author Share Posted September 2, 2019 8 hours ago, Ghideon said: It looks like the problem could have been based on other number but author picked x=8. Isn't θ is the angle at the lighthouse L between lines LQ and LP? Then x=8 is the opposite and 10 is the adjacent. tanθ=opposite/adjacent or tanθ=x/10 so x=10tanθ Hint regarding the derivatives: are you familiar with the chain rule for computing the derivative of the composition of two (or more) functions? Thanks for the help. Yes, I am familiar with composition of functions and the chain rule. It's just that word problems are hard for me. Link to comment Share on other sites More sharing options...
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