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Unformatted text preview: Chapter 11 Relative Velocity 62 11 Relative Velocity Vectors add like vectors, not like numbers. Except in that very special case in which the vectors you are adding lie along one and the same line, you can’t just add the magnitudes of the vectors. Imagine that you have a dart gun with a muzzle velocity 1 of 45 mph. Further imagine that you are on a bus traveling along a straight highway at 55 mph and that you point the gun so that the barrel is level and pointing directly forward, toward the front of the bus. Assuming no recoil, as it leaves the muzzle of the gun, how fast is the dart traveling relative to the road? That’s right! 100 mph. The dart is already traveling forward at 55 mph relative to the road just because it is on a bus that is moving at 55 mph relative to the road. Add to that the velocity of 45 mph that it acquires as a result of the firing of the gun and you get the total velocity of the dart relative to the road. This problem is an example of a class of vector addition problems that come under the heading of “Relative Velocity.” It is a particularly easy vector addition problem because both velocity vectors are in the same direction. The only challenge is the vector addition diagram, since the resultant is right on top of the other two. We displace it to one side a little bit in the diagram below so that you can see all the vectors. Defining BR v h to be the velocity of the bus relative to the road, DB v h to be the velocity of the dart relative to the bus, and DR v h to be the velocity of the dart relative to the road; we have The vector addition problem this illustrates is DR v h = BR v h + DB v h If we define the forward direction to be the positive direction, then, because the vectors we are adding are both in the same direction, we are indeed dealing with that very special case in which the magnitude of the resultant is just the sum of the...
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.
- Fall '08