The image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 25 / 3 ~m to 50 / 7 ~m in 30 second. The speed of the object in km / hr is

Step-by-step solution

Convex Mirror Problem Solution Using the mirror formula 1 f = 1 v + 1 u where focal length f = R/2 = 10 m (positive by convention). For initial image position v₁ = 25/3 m: 1 u₁ = 1 10 - 3 25 = - 1 50 u₁ = -50 m For final image position v₂ = 50/7 m: 1 u₂ = 1 10 - 7 50 = - 1 25 u₂ = -25 m The object moves from u₁ = -50 m to u₂ = -25 m, covering distance u = 25 m in 30 seconds. Speed is 25 30 = 5 6 m/s. Converting to km/h: 5 6 18 5 = 3 km/h The object's speed is 3 km/h.