Derivative problem

  • Thread starter kristo
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  • #1
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Homework Statement


A plane starts its descent from height y=h at x =-L to land at (0,0). Choose a, b, c, d so its landing path y=ax^3 + bx^2 + cx + d is smooth.With dx/dt=V=constant, find dy/dt and d2y/dt2 at x=0 and x =-L. (To keep d2y/dt2 small, a coast-to-coast plane starts down L>100 miles from the airport.)

The Attempt at a Solution


For a smooth landing the derivative must be negative and 0 at x=0.
y'=3ax^2+2bx+c < 0
y'(0)=0
c=0
d must be 0 because y(0)=0.
second derivative must be > 0.
y''=6ax+2b >0

And that's as far as I get. I'd appreciate any tips and can someone explain to me how dx/dt can be constant? And how do I find dy/dt?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
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Merry Christmas!

… can someone explain to me how dx/dt can be constant? And how do I find dy/dt?

Hi kristo! :smile:

Think of the curve as a hillside … the driver can drive at whatever speed he likes.

And to find dy/dt, use the chain rule. :wink:
 

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