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Physics Tools Physics for the Life Sciences Lecture #1B Racquetball Striking a Wall Mt. Etna Stewart Hall
A Nice Way to Use Vectors •Relative velocity: sometimes a velocity is ‘made up’ of several parts: you walk through a train while it moves over the track •Your total velocity is a sum of several components vperson-ground=vperson-train+vtrain-groundvperson-trainvtrain-groundvtrain-groundvperson-trainvperson-groundyxzvPG=vPT+vTGOR
In Two Dimensions It’s the Same •Imagine a dog swimming across a river •The dog swims at 1.2 [m/s] relative to the water •The water flows left at 1.2 [m/s] •If the dog “heads straight across” (swims relative to the waterwith his nose pointing to the opposite shore), it travels at 45º relative to the shore. vdog-watervdog-shorevwater-shorevdog-watervwater-shorevdog-shore=vdog-water+vwater-shoreor vDS=vDW+vWSyxz
•Imagine a dog swimming across a river oThe dog can swim at 2 [m/s] relative to the water oThe water flows West at 1 [m/s] relative to the shore •What direction must the dog swim to end up directly across the river as shown? To move straight across the velocity of the dog relative to the shore must aim directly across the river (he must add a component of its velocity vector 1 [m/s] to the right so as to produce a zerovelocity component parallel to the river bank). N E Question #2 vdog-shorevwater-shorevdog-shorevdog-water±θ=cos−112⎡⎣⎢⎤⎦⎥vwater-shore(A) He cannot swim directly across (B) 60oSouth of East (C) 30oSouth of East
Experiment: Velocity Vectors and Relative Motion The toy car shown will move under its own power at a constant speed. Let’s define the xdirection to be along the lab bench to the right as seen from your seat. The y coordinate will be toward the blackboard. Now we’ll place