How Fast is the Plane Flying in the Derivative Problem?

[Sirius_GTO]

An airplane is flying on a flight path that will take it directly over a radar tracking station. If (s) is decreasing at a rate of 400 miles per hour when s=10 miles, what is the speed of the plane?

Can someone explain in indepth response including reasons why each steps were taken. Thank you!

 

[Sirius_GTO]

I also need help with this problem.

 

[HallsofIvy]

Well, both pictures look pretty much like right triangles don't they? So the Pythagorean theorem applies. In the first one, at any time t, the vertical distance is the constant 6 miles. The horizontal distancd is the function x(t) and the straight line distance is the function s(t). Using the Pythagorean theorem, x^{2+ 62= s2. Differentiate both sides of the equation with respect to t to get a relationship between the rates of change.}

 

[Sirius_GTO]

Thanks a lot for your help Doc.

As for the 2nd problem, I noticed that in the book they find that the height of the rocket when t=10 is 5000 feet. Exactly how did they find this?

 

[HallsofIvy]

Reread the problem. Unless the problem itself gives some information on how fast the rocket is going up, or the "5000 ft" is given in the problem, there is no way to do that.

 

[Sirius_GTO]

OI, in the description it gave the formula 50t^2...

I didn't even see that...