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Math Help - relative motion

  1. #1
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    relative motion

    Im trying to help my daughter and we are lacking information like a formula for relative velocity.. here is one of 20 problems and I am wishing someone could explain it enough that we can learn and do the rest. Thanks

    Two cars are traveling inthe same direction. Car A is traveling 62mph. Car B is traveling 70mph. When car B passes car A, how fast does car b appear to be going to the passengers in car A? How much slower does car A appear to be going to the passengers of car B?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by roxig66 View Post
    Im trying to help my daughter and we are lacking information like a formula for relative velocity.. here is one of 20 problems and I am wishing someone could explain it enough that we can learn and do the rest. Thanks

    Two cars are traveling inthe same direction. Car A is traveling 62mph. Car B is traveling 70mph. When car B passes car A, how fast does car b appear to be going to the passengers in car A? How much slower does car A appear to be going to the passengers of car B?
    The best way to look at these is to try to visualize the problem. Car B is moving in the same direction, so we automatically know that car B should be moving slower in the frame of car A than it is in the stationary (groud based) frame. Let that be your guide:
    v = 70 mph - 62 mph = 8 mph

    If you really want the formulae then I have to introduce some variables for you. Let us have two people: Stacy and Moe, and one moving object. We're going to put Stacy in the "stationary" frame, that is the one that isn't moving relative to the ground. We're going to assume Moe ("moving" frame) is moving at a constant velocity v (according to Stacy) relative to Stacy in the stationary frame.

    Let the object be moving at a velocity vS according to Stacy and moving at velocity vM according to Moe.

    Then
    vS = vM + v

    Note that these are all velocities and hence vector quantities, so this is a vector addition.

    To apply this to your car problem, car B is your object, car A is Moe. Calling the direction of car A relative to the ground to be positive we have:
    v = 62 mph (the velocity of car A relative to the ground)
    vS = 70 mph (the velocity of car B relative to the ground)
    vM = ? (the velocity of car B relative to car A)

    vS = vM + v
    70 mph = vM + 62 mph
    vM = 70 mph - 62 mph = 8 mph
    as I stated earlier.

    -Dan
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    thank you

    Thank you for the reply last night it helped my daughter understand relative motion problems more clearly. She was able to go and complete all of her application problems unassisted.

    Roxanne
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by roxig66 View Post
    Thank you for the reply last night it helped my daughter understand relative motion problems more clearly. She was able to go and complete all of her application problems unassisted.

    Roxanne
    Pleased to be of service!

    -Dan
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