Calculus and Trig Problem?

[Metume]

Hello, I have been at this problem for days now I am don’t know how to solve with calculus, I am supposed to solve how calculus can be applied here ;-;. Help and a thorough explanation would be greatly appreciated. Thank you!

 

[skeeter]

Make a sketch, label fixed and variable lengths, then set up an equation using a trig ratio.

Differentiate implicitly w/respect to time.

 

[Deleted member 4993]

Hello, I have been at this problem for days now I am don’t know how to solve with calculus, I am supposed to solve how calculus can be applied here ;-;. Help and a thorough explanation would be greatly appreciated. Thank you! View attachment 27810

If I were to do this problem, I would first:

Sketch the situation (will be triangle/s) approximately and assign name/s to the appropriate part/s.

Which angle (referring to the sketch) is the angle of elevation?

Post (a photograph of) the sketch

Please show us what you have tried and exactly where you are stuck.​

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[Metume]

Hello, I have been at this problem for days now I am don’t know how to solve with calculus, I am supposed to solve how calculus can be applied here ;-;. Help and a thorough explanation would be greatly appreciated. Thank you! View attachment 27810

Thai’s is what I have so far:

Make a sketch, label fixed and variable lengths, then set up an equation using a trig ratio.

Differentiate implicitly w/respect to time.

 

[skeeter]

[MATH]\theta[/MATH] is a variable.

[MATH]\cot{\theta} = \dfrac{x}{5000}[/MATH]
Take the derivative w/respect to time, then substitute the given values for [MATH]\theta[/MATH] and [MATH]\frac{d\theta}{dt}[/MATH].

Finally, solve for [MATH]\frac{dx}{dt}[/MATH].

 

[Steven G]

The angle is NOT pi/4! The angle is changing! You are giving information about when the angle is pi/4.
Set up your equation with the angle being say theta, not the constant pi/4. See where you can go from there.
This is what skeeter suggested.

 

[Metume]

[MATH]\theta[/MATH] is a variable.

[MATH]\cot{\theta} = \dfrac{x}{5000}[/MATH]
Take the derivative w/respect to time, then substitute the given values for [MATH]\theta[/MATH] and [MATH]\frac{d\theta}{dt}[/MATH].

Finally, solve for [MATH]\frac{dx}{dt}[/MATH].

Thank you

The angle is NOT pi/4! The angle is changing! You are giving information about when the angle is pi/4.
Set up your equation with the angle being say theta, not the constant pi/4. See where you can go from there.
This is what skeeter suggested.

Thank you