A car is fitted with a convex sideñview mirror of focal length 20 cm.Asecond car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is

1/15 m/s

10 m/s

15 m/s

1/10 m/s

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Solution

1/15 m/s

The mirror formula

1 over straight u space plus 1 over straight v space equals space 1 over straight f 1 over straight v space plus space fraction numerator 1 over denominator negative 280 end fraction space equals space 1 over 20 1 over straight v space space equals space 1 over 20 plus 1 over 280 1 over straight v space plus fraction numerator 14 plus 1 over denominator 280 end fraction straight v space equals space 280 over 15 straight v subscript 1 space equals space minus space open parentheses straight v over straight u close parentheses squared. straight v therefore space straight v subscript 1 space equals space minus open parentheses fraction numerator 280 over denominator 15 space straight x space 280 end fraction close parentheses squared.15 space therefore space equals space straight v subscript 1 space equals space fraction numerator negative 15 over denominator 15 space straight x space 15 end fraction straight v subscript 1 space equals space minus 1 over 15 space straight m divided by straight s

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