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Homework Help: Assistance needed with vector velocity problem, please

  1. Sep 19, 2008 #1
    An asteroid is discovered heading straight toward Earth at 15 km/s. An international team manages to attach a giant rocket engine to the asteroid. The rocket fires for 10 min, after which the asteroid is moving at 28[tex]\circ[/tex] to its original path at a speed of 19 km/s.

    Find its average acceleration (ax, ay) in m/s2.

    I first began by using the equation a2 = b2 + c2 -2bc(cos[tex]\alpha[/tex]) where b is 15 km/s and c is 19 km/s.

    a2 = 225 + 361 - 570(cos28[tex]\circ[/tex])
    a2 = 82.7 km/s
    9.1 km/s m= [tex]\Delta[/tex]v

    a= 9.1 / 600 = .0152 km/s2 = 15.2 m/s2


    The answer is [tex]r\hat{}[/tex] = (3.0[tex]i\hat{}[/tex] + 15 [tex]j\hat{}[/tex]) m/s2.

    I am unsure as to whether or not I have done this correctly because I do not know where to go from here. My professor gave use this hint for this problem:

    The asteroid is initially going in the +x direction! From the given initial and final
    velocities, find [tex]\Delta[/tex]vx and [tex]\Delta[/tex] vy. Use ax = [tex]\Delta[/tex]vx/[tex]\Delta[/tex]t and ay = [tex]\Delta[/tex]vy/[tex]\Delta[/tex]t
     
    Last edited: Sep 19, 2008
  2. jcsd
  3. Sep 19, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi SelHype! Welcome to PF! :smile:

    The question asks for (ax, ay).

    Your cosine formula only gave you the magnitude, |a| (which was correct :wink:) …

    but you won't get the direction without using the sine formula also, which is far too long-winded a method.

    There are two ways of dealing with vectors … the good old trigonometry way that the ancient Greeks would have used, and the coordinate method.​

    You've used the slow ancient Greek way.

    Your professor wants you to use the quicker coordinate way. :wink:

    Do what your professor suggested … :smile:
     
  4. Sep 20, 2008 #3
    Re: Welcome to PF!

    Thank you for the welcome!

    I should have known I was doing it the long way, haha. I am VERY bad for going the more complicated routes because...well they seem easier...Yeah I'm odd.

    But thank you for the help! I finally got it after I looked at it for bout another hour, haha.

    Anyways, thanks again!
     
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