InterviewSolution
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InterviewSolution
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A car is fitted with a convex side-view mirror of focal length 20 cm. A second car 2.8m 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 mrror of the first one is:A. `-(1)/(15)m//s`B. `10 m//s`C. `15 m//s`D. `(1)/(10) m//s` |
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Answer» Correct Answer - A From mirror formula (using convex mirror) `(1)/(u) + (1)/(v) = (1)/(f)` …(i) Using `u = - 2.8 m = -280 cm, f = 20 cm` `:. (1)/(- 280) + (1)/(v) = (1)/(20) or (1)/(v) = (1)/(20) + (1)/(280) = (15)/(280)` or `v = (280)/(15)cm` Differentiating (i) w.r.t `t`, we have `-(1)/(u^(2))(d u)/(dt) - (1)/(v^(2))(dv)/(dt) = 0` or `(d v)/(dt) = -(v^(2))/(u^(2))((d u)/(dt))` `:.` Relative velocity of image, `v_(1) = (d v)/(dt) = -(v^(2))/(u^(2))((d u)/(dt)) = (- (280 //15^(2)))/((-280)^(2)) xx 15` `= -(1)/(15)m//s` |
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