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A car is fitted with a convex side-view mirror of focal length 20cm. A second car 2.8 m behind the first car is overtaking the first car at 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

A car is fitted with a convex side-view mirror of focal length 20cm. A second car 2.8 m behind the first car is overtaking the first car at 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

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
2 years ago
576-1852_2.PNG
Vikas TU
14149 Points
2 years ago
From mirror formula (using convex mirror)
1/u+1/v=1/f …(i)
Using u=−2.8m=−280cm,f=20cm
∴1/−280+1/v=1/20or1/v=1/20+1/280=15/280
or v=280/15cm
Differentiating (i) w.r.t t, we have
−1/u2du/dt−1/v2dv/dt=0 or dv/dt=−v2/u2(du/dt)
∴ Relative velocity of image,
v1=dv/dt=−v2/u2(du/dt)=−(280/152)/(−280)2×15
=−1/15m/s

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