related rates

[autumn drift]

A plane flying with a constant speed of 240 km/h passes over a ground radar station at an altitude of 2 km and climbs at an angle of 30°. At what rate is the distance from the plane to the radar station increasing a minute later? (Round your answer to the nearest whole number.)
km/h

[devout lance]

first step of related rates is to get a function that gives the distance at a given moment

so, lets start with that

what can we use to determine the distance?

[autumn drift]

distance formula ig

[devout lance]

yea

and then, what two values are the sides of the right triangle

[autumn drift]

240 & 2?

[devout lance]

well, the airplanes position changes as a function of time, no?

so, can you get the coordinates of it for t minutes or hours, depending on what you like, after it is at 240,2?

[autumn drift]

honestly u lost me

i am so utterly confused

[devout lance]

how did you learn related rates btw

[autumn drift]

i just learned em yesterday but it was confusing as anything

[devout lance]

i learned it the wrong way after someone tried to teach me the correct way :P

but its more effective for me

just confusing to others

[autumn drift]

@devout lance ??? sorry im so lost

[devout lance]

okay, so uhhh

what would be the coordinates of the plane after 1 hour

and keep in mind the calculation you do to get that

then try getting 2 hours, half hour, etc., see if you notice a pattern

and that might help you find a general form for the coordinates of the plane

[autumn drift]

🤷‍♂️

[autumn drift]

idk the calculation

[devout lance]

okay lets draw a diagram to help us out here

how familiar are you with coordinates

like if i did coordinate geometry here would that confuse you

so the plane is 2 km above

n stuff

now if the angle there is 30, how can we find the general equation of the line

[autumn drift]

🤷‍♂️

irdk

[devout lance]

okay lets swap to the other type of related rate solving

well its basically the same thing buy

but*

we draw a right angle from the base to the airplane, right now, it has a side of 0 and 2...

so now we want to find at what rate these sides are increasing

[autumn drift]

@devout lance whered u get 0 from? im utterly confused respectfully

[devout lance]

okay yea thats fair

so we can make a right triangle

one leg is the horizontal distance from the plane to the base

the other is the vertical distance

right?

[autumn drift]

@devout lance nvm i finally got the answer but ty

[tardy lava]

@autumn drift has given 1 rep to @devout lance

[devout lance]

yay! gj

[autumn drift]

thanks but i still have no idea what im doing

the website had a video with a problem similar so i just did what that person did

[tardy lava]

@autumn drift has given 1 rep to @devout lance

[devout lance]

you can check khan academy for some nice course stuff

[autumn drift]

thanks