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A thief is running away in his car with a velocity of 20m/s.A police jeep is following him which is sighted by the thief in his rearview mirror, a convex mirror of focal length 10m.He observes that the jeep is moving towards him with a speed of 1cm/s.If the magnification of the mirror for the jeep at that time is 1/10. Find: 1. actual speed of the jeep 2. rate at which magnification is changing
Hiii rom the mirror formula 1/v +1/u = 1/f We get the velocity of image as :Vi = m^2 * Vo Vo = Relative velocity of object with respect to mirrorVi = Relative velocity of imagem = Linear magnification.Vo = v – 20 Vi = 1cm/secm = 1/10Put the value in equation above.v = 21m/secBy the mirror formula we can write as 1/m = (u-f)/fm = f/(u-f)dm/dt = -f/(u-f)2 . du/dtput value of m and find u u = -90mput the value of u in differential equation.dm/dt = 0.001 per second.
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