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A ball is approaching a convex mirror of focal length 30 cm with speed 20 m//s. Calculate the speed of its image when the ball was at 5 m from the mirror? |
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Answer» Solution :We have mirror equation `1/f=1/u+1/v` `1/v=1/f-1/u` `v=(fu)/(u-f)` Differentiate w.r.t .t. `(DV)/(dt)=(f)/((u-f))(du)/(dt)-(fu)/((u-f)^2)(du)/(dt)` `(dv)/(dt)=(du)/(dt)[(f)/(u-f)-(fu)/((u-f)^2)]` Here: `(du)/(dt)= 20ms^(-1)`, f = 30cm=0.3m u = -5m `(dv)/(dt)=20[(0.3)/(-5-0.3)-(0.3(-5))/((-5-0.3)^2)]` `=20[(90.3)/(-5.3)+(1.5)/((-5.3)^2)]` = 20[-0.0566 + 0.0534] `(dv)/(dt)=20[-0.0032]= -0.064 ms^(-1)` |
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