Annoying related rates / trig problem

[Jwmphall2]

Attached is a problem I received in calc ii if anybody knows how to do it please assist. I can’t seem to relate the position relative to the observer with the constantly changing angle and R.

 

[Deleted member 4993]

Attached is a problem I received in calc ii if anybody knows how to do it please assist. I can’t seem to relate the position relative to the observer with the constantly changing angle and R.

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

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

 

[Jwmphall2]

Bro you

I cannot read the attachment - it is extremely faint and small.

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

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Bro you need better eyes.

 

[skeeter]

I recommend using the cosine law ...

[MATH]a^2=b^2+c^2-2bc \cos{\theta}[/MATH]

 

[Dr.Peterson]

Attached is a problem I received in calc ii if anybody knows how to do it please assist. I can’t seem to relate the position relative to the observer with the constantly changing angle and R.
View attachment 23454

You could introduce coordinates, writing the position of the aircraft as a function of time, and using the distance formula.

It will also help if you show some work, so we can see what method you are trying, and what (if anything) is going wrong.

 

[Harry_the_cat]

Bro you

Bro you need better eyes.

Bro, you need to get some manners.

 

[skeeter]

Attached is a problem I received in calc ii if anybody knows how to do it please assist. I can’t seem to relate the position relative to the observer with the constantly changing angle and R.

The angle, [MATH]\theta[/MATH], of the aircraft’s velocity relative to the ground is constant, i.e. not changing.

As stated earlier, use the cosine law to get [MATH]R[/MATH] in terms of [MATH]v, \, t, \theta, \text{ and }R_i[/MATH]. You can then find [MATH]\dfrac{dR}{dt}[/MATH] and determine the time when [MATH]R[/MATH] is a minimum.

To check your calculus solution, note that the aircraft’s closest position to the observer forms a right triangle, where the distance [MATH]R[/MATH] between the observer and aircraft is perpendicular to the aircraft’s path of travel. As such, one can solve the time of that position in terms of [MATH]v, \, \theta, \text{ and }R_i[/MATH] using a right triangle trig ratio with [MATH]\theta[/MATH].