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Figure 3.19a shows two cars approaching an intersection along perpendicular roads. The cars have the following velocities:
Find the magnitude and direction of vAB, where
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Two cars are approaching an intersection along perpendicular roads. |
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Reasoning
To find vAB, we use an equation whose subscripts follow the order outlined earlier. Thus,
In this equation, the term vGB is the velocity of the ground relative to a passenger in car B, rather than vBG, which is given as 15.8 m/s, northward. In other words, the subscripts are reversed. However, vGB is related to vBG according to
This relationship reflects the fact that a passenger in car B, moving northward relative to the ground, looks out the car window and sees the ground moving southward, in the opposite direction. Therefore, the equation vAB =vAG+vGB may be used to find vAB, provided we recognize vGB as a vector that points opposite to the given velocity vBG. With this in mind, Figure 3.19 illustrates how vAG and vGB are added vectorially to give vAB.
Problem solving insight
In general, the velocity of object R relative to object S is always the negative of the velocity of object S relative to R: vRS=–vSR |
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Solution
From the vector triangle in Figure 3.19b, the magnitude and direction of vAB can be calculated as
and
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