Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ieatpi

  • 2 years ago

A space probe is shot upward from the earth. If air resistance is disregarded, a differential equation for the velocity after burnout is v dv/dt = -ky^-2, where y is the distance from the center of the earth and k is a positive constant. If y0 is the distance from the center of the earth at burnout and v0 is the corresponding velocity, express v as a function of y.

  • This Question is Closed
  1. hal_stirrup
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    write the equation again am not sure what am reading is right.

  2. ieatpi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[v \frac{ dv }{ dt } = -ky ^{-2} \]

  3. ieatpi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits_{}^{}Vdv = \int\limits_{}^{} -ky ^{-2}dy\]\[\frac{ 1 }{ 2 }V ^{2}=ky ^{-1} + c\]\[V=\sqrt{2k \frac{ 1 }{ y } + c}\] So having done that, does c turn in to the initial velocity?

  4. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    except that it is dt not dy I was thinking V= dy/dt so you could say dt= dy/V and sub in for dt in the equation.

  5. ieatpi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    typo, should be dy

  6. phi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that makes it easier. to find c, plug in V0 for V and Y0 for y in your 2nd equation and solve for c

  7. ieatpi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok I'll give that a shot, thanks!

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.