1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Speed in A Plane Mirror

  1. Nov 28, 2012 #1
    Suppose a driver his reversing his car with a speed of 2m/s, the driver sees in his rear-view mirror (which is a plane mirror) the image of a truck parked behind his car. What will be the speed at which the image of the truck appears the driver?

    According to me, since the distance between the car and truck is equal to their distance in the mirror (because its a plane mirror), the speed at which the image appears should also be 2m/s, but the answer behind the Olympiad book says something else and I can't really figure out any other way to think about this problem.

    Thanks
     
  2. jcsd
  3. Nov 28, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Say you are a distance 2D from the mirror. How far away does the image appear?
    What if you were a distance D from the mirror?
     
  4. Nov 28, 2012 #3
    In the first case 4D. In the second case 2D.
    Ah, I see.... Just as the car approaches the truck, so does the image of the car in the mirror, therefore the apparent distance covered is 2 times the actual distance covered by the car.
    So, can we conclude that since

    2 = d/t, 2d/t= 2(2)=4 ?
     
  5. Nov 28, 2012 #4

    jbriggs444

    User Avatar
    Science Advisor

    What frame of reference are you trying to use?

    From the point of view of the driver, the image in his rear-view mirror will approach at a speed of 2 meters per second. I agree with you on this.

    From the point of view of a physicist standing by with a pencil, a piece of paper and an optics textbook the virtual image in the mirror will move at a speed of 4 meters per second relative to the ground.

    From the point of view of the driver, the image in his rear view mirror will be approaching at an apparent speed of 2 meters per second as above while the ground viewed through his windshield is receding at a speed of 2 meters per second. This adds up to a closing rate of 4 meters per second. [The distinction between a speed and a closing rate is a not important if we're sticking to classical physics]
     
  6. Nov 28, 2012 #5

    Doc Al

    User Avatar

    Staff: Mentor

    I agree with that. (My earlier post was irrelevant, since it's the driver's frame that we are after.)

    What did the book say that differed?
     
  7. Nov 28, 2012 #6

    sophiecentaur

    User Avatar
    Science Advisor
    Gold Member

    I am not too happy with these conclusions (or I may be misunderstanding).
    I see it this way.
    The image distance is equal to the object distance therefore the image speeds will be the same. To a ground based observer, the two will be approaching each other with velocities of +2 and -2 respectively. To the driver, the image will be approaching at 4.
    I'm assuming that the motion is normal to the plane of the mirror, for simplicity.
     
  8. Nov 28, 2012 #7

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The two what, exactly?
    A bystander (at the truck, say) will see the car and its mirror approaching at 2m/s, and see the image as catching the car up at 2m/s, for a total of 4m/s.
    The driver is not being approached by the mirror, so only sees the 2m/s motion of the image relative to the mirror.
     
  9. Nov 29, 2012 #8

    sophiecentaur

    User Avatar
    Science Advisor
    Gold Member

    I can be so dumb sometimes. I was back at school with a mirror on the bench and not in the car with a driving mirror. My frame of reference was all to hell!! What would the legendary Mr Scales have said?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook