Thread: Need Calc 1 Help.

1. A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 8 km and climbs at an angle of 50 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 1 minutes later?


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2. A particle is moving along the curve y=2*sqrt(5x+1). As the particle passes through the point (38), its x-coordinate increases at a rate of 4 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

This is a good set of problems.
What have you done on them?
If you try them then you are bound to learn a great deal.
But if we do them for you, you learn little.

I have done about 16 of these and these are the ones that have me stumped...I can get started and get an answer but its always incorrect.

Hello, lmao!

I'll walk through the first one . . .
And I'm changing the units to miles and miles per hour, okay?

1. At noon, ship A is 50 miles due west of ship B.
Ship A is sailing west at 25 mph and ship B is sailing north at 18 mph.
How fast is the distance between the ships changing at 7 PM?

Code:

                              * B
                          *   |
                 x    *       |
                  *           | 18t
              *               |
          *                   |
      * - - - - * - - - - - - *
      A   25t   P     50      Q

At noon, ship A starts at point P, 50 miles west of point Q.
. . At 25 mph, in the next t hours, it moves 25t miles to point A.

At noon, ship B start at point Q, sailing north at 18 mph.
. . In the next t hours, it moves 18t miles to point B.

Let x = the distance AB.

Pythagorus says: .x² .= .(25t + 50)² + (18t)²

So we have: .x² .= .949t² + 2500t + 2500

Differentiate with respect to time: .2x(dx/dt) .= .1898t + 2500

. . and we have: .dx/dt .= .(1898t + 2500)/2x .[1]


At 7 PM (t = 7): .x² .= .949·7² + 2500·7 + 2500 .= .66,501
. . Hence: .x .= .√(66501)


Substitute into [1]: .dx/dt .= .(1898·7 + 2500)/(2√66501) .≈ .30.6 mph

Now you can change it back to "knots" . . .

Excellent explanation. Thank you so much!

I know I am not an Admin but I have seen this exact post twice already, whats up with the double posting?

Yeah my bad, I'll delete the other one if it lets me. I posted there then realized there was a urgent help forum. Sorry again!

RE:

I can tell this is WebWorks problem, thus I am going to help you with 1 of them.

#4.

I solved #2 so I'll take that one out. Thanks for understanding that webwork is a pain. So #1,2,4 are now done. Two more! Thanks guys!!

Originally Posted by lmao

1. A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 8 km and climbs at an angle of 50 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 1 minutes later?

Here. As I always say, ALWAYS DRAW A DIAGRAM WHEN DOING A RELATED RATES PROBLEM.

related rates 1 is the solution
related rates 1b is the diagram i used to think about a solution

RE: Sorry I made an error, its getting late...UPDATE

All of them are complete! Thanks everyone for helping.