Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathslover

A dog chasing the cat who is running along a striaght line at constant speed u . The dog moves with constant speed v, always heading towards the cat. Initially i.e. at t = 0 , the velocity of the dog and the cat are perpendicular and then initial perpendicular distance between them is 1. The dog catches the cat at ?

  • one year ago
  • one year ago

  • This Question is Closed
  1. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    @Callisto

    • one year ago
  2. AravindG
    Best Response
    You've already chosen the best response.
    Medals 0

    This is one of the classic questions on this topic .But I have to leav now .can definitely answer tomorrow is that OK @mathslover ?

    • one year ago
  3. abb0t
    Best Response
    You've already chosen the best response.
    Medals 0

    If they are perpendicular, that meas they intresect at a 90º angle. the distance between them (i think hypotenusre) = 1

    • one year ago
  4. abb0t
    Best Response
    You've already chosen the best response.
    Medals 0

    How did I end up in physics section Lol.

    • one year ago
  5. shubhamsrg
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1359311516476:dw| Let time taken be t, then (v cosx) t = 1 ...(1) u = vsinx ..(2) Just eliminate x to solve for t

    • one year ago
  6. shubhamsrg
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh wait, am missing on the fact that x is a variable.

    • one year ago
  7. shubhamsrg
    Best Response
    You've already chosen the best response.
    Medals 0

    Getting too late here, I will get back to it later.

    • one year ago
  8. UnkleRhaukus
    Best Response
    You've already chosen the best response.
    Medals 0

    is \(u>v,\quad u=v,\quad \text{or}\quad u<v\) ?

    • one year ago
  9. shubhamsrg
    Best Response
    You've already chosen the best response.
    Medals 0

    u<v (since dog is always heading towards cat) , I guess.

    • one year ago
  10. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 0

    I am curious to see Aravind's solution. It's not hard to write down the equations of motion here. But solving them is not so obvious.

    • one year ago
    1 Attachment
  11. AravindG
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathslover do you have final answer ? I wanted to check before replying

    • one year ago
  12. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 0

    Two major objections 1. The first one is the answer doesn't make sense. Suppose the velocities u and v are equal. Then it is clear the dog never reaches the cat. But according to the formula you have ended up with, the dog catches the cat in finite time of \[ t = \frac{\sqrt{v^2 + u^2}}{v^2} = \frac{\sqrt{2}v}{v^2} = \frac{\sqrt{2}}{v} \] 2. The second one is you haven't explained your reasoning very well at all and there appear to be errors in the calculation. For instance, why does the angle theta between their velocity vectors--or the y component of it--satisfy cos theta = v/sqrt(v^2 + u^2)? Or why does (v - u) cos theta = (v - u) . v / sqrt(v^2 + u^2) imply something (their relative velocity in the y direction?) equals v^2/sqrt(v^2 + u^2)? And even if that were true, just because the relative displacement of two moving objects is <0,1>, by what kinematic equation is it the case that their relative velocity in the y direction can be directly deduced from that initial relative displacement, given that it is immediately clear that their relative displacement changes over time? ***** So I am not satisfied we have the solution.

    • one year ago
  13. abb0t
    Best Response
    You've already chosen the best response.
    Medals 0

    yoloswag

    • one year ago
  14. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 0

    But it is clear that the dog is NOT moving in a straight line. The dog is constantly changing direction.

    • one year ago
  15. harsh314
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks @jamesJ i got it the time period is \[\frac{ v }{ {v ^{2}-u ^{2}} }\]

    • one year ago
  16. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    I got it now , Thanks a lot every one...

    • one year ago
  17. harsh314
    Best Response
    You've already chosen the best response.
    Medals 1

    and once again thanks to @mathslover for giving such a nice question keep it up!!

    • one year ago
  18. mathslover
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks @harsh314 Just hope that I get a doubt soon in such a problem :)

    • one year ago
  19. harsh314
    Best Response
    You've already chosen the best response.
    Medals 1

    may god bless you with such capabilites that you never get stuck in any question but for the sake of enrichment of our knowledge'thanks

    • one year ago
  20. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 0

    Wait. We still don't have a good solution to this problem. Harsh has written down a solution. But where's the proof?

    • one year ago
    • Attachments:

See more questions >>>

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.