Question

A particle is dropped along the axis from a height 15 cm on a concave mirror of focal length 30 cm as shown in figure. The acceleration due to gravity is 10 m/s². Find the maximum speed of image in m/s:

Options

• 1.2 m/s

• 3.5 m/s

• 2.25 m/s

• 5.5 m/s

Answer 1

2.25 m/s

Explanation:

`("d"x"i")/"dt" = -("f"/("f"-x_0))^2("d"x_0)/"dt"`

v_xi = `-[(-"f")/(-"f"+("f"/2-"y"))]^2sqrt(2"gy")`

`("dv"_(x"i"))/"dy" = 0`

⇒ y = `"f"/6`

∴ v_xi = `3/4sqrt(3 "fg")`

= `3/4sqrt(3xx0.3xx10)`

= `9/4`

= 2.25 m/s