# Need Calc 1 Help.

• Apr 15th 2007, 03:35 PM
lmao
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?

------------------------------------------------------------------------

2. A particle is moving along the curve y=2*sqrt(5x+1). As the particle passes through the point (3https://webwork.math.uga.edu/webwork...144/char3B.png8), 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.
• Apr 15th 2007, 03:40 PM
Plato
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.
• Apr 15th 2007, 03:44 PM
lmao
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.
• Apr 15th 2007, 04:19 PM
Soroban
Hello, lmao!

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

Quote:

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: . .= .(25t + 50)² + (18t)²

So we have: . .= .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): . .= .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" . . .

• Apr 15th 2007, 04:48 PM
lmao
Excellent explanation. Thank you so much!
• Apr 15th 2007, 05:04 PM
qbkr21
Re:
I know I am not an Admin but I have seen this exact post twice already, whats up with the double posting?
• Apr 15th 2007, 05:24 PM
lmao
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!
• Apr 15th 2007, 05:24 PM
qbkr21
Re:
RE:

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

#4.
• Apr 15th 2007, 05:39 PM
lmao
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!!
• Apr 15th 2007, 06:42 PM
Jhevon
Quote:

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
• Apr 15th 2007, 06:44 PM
qbkr21
Re:
RE: Sorry I made an error, its getting late...UPDATE
• Apr 15th 2007, 06:54 PM
lmao
All of them are complete! Thanks everyone for helping.