A Toyota Prius driving north at 58.0mph and a VW Passat driving south at 40.0mph

Question

A Toyota Prius driving north at 58.0mph and a VW Passat driving south at 40.0mph are on the same road heading toward each other (but in different lanes). (We take the positive direction to be north.)

What is the velocity of Toyota Prius relative to the VW Passat when they are 350 ft apart, just before they meet?

What is the velocity of VW Passat relative to the Toyota Prius when they are 350ft apart, just before they meet?

What is the velocity of Toyota Prius relative to the VW Passat when they are 520 ft
apart, after they have passed each other?

What is the velocity of VW Passat relative to the Toyota Prius when they are 520 ft apart, after they have passed each other?

Explanation / Answer

a) Relative to the VW Passat, the Toyota Prius is traveling at 104.0 mph to the north.  Think of it as if you were sitting in the VW Passat.  When the Toyota Prius passes you, it appears to be moving at its speed (62.0 mph) plus the speed that you're moving past it (42.0 mph).  It is moving north because you are moving south and it is moving the opposite direction as you.  So its velocity is 104 mph.

b) Relative to the Toyota Prius, the VW Passat is traveling at 104.0 mph to the south.  So its velocity is -104 mph.

c) Relative to the VW Passat, the velocity of the Toyota Prius is still 104 mph

d) Relative to the Toyota Prius, the velocity of the VW Passat is still -104 mph.

 

Hope this helps! ... and hopefully, I'm right.  That seemed way too easy..

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