An object is kept on the principal axis of a convex mirror of focal length `10 cm` at a distance of `10 cm` from the pole. The object starts moving at a velocity `20 mm//sce` towards the mirror at angle `30^(@)` with the principal axis. What will be the speed of its image and direction with the principal axis at that instant.

Options

A. speed `=5 (sqrt7)/(4)mm//sec`
B. speed `=(5 sqrt7)/(2)mm//sec`
C. `tan^(-1) ((2)/(sqrt3))` with the principal axis
D. none of these

Answer

B, C

Explanation

We have `v=(vf)/(u-f)=((-10)(10))/(-10-10)=+5`
`therefore v_(ix)=-(v^(2))/(u^(2))v_("ox")`
`=-((5)/(-10))^(2)xx20.(sqrt2)/(2)=-(5sqrt3)/(2) mm//sec`
and `v_(iy)=-((v)/(u))v_(oy)=-((5)/(-10))xx20xx(1)/(2)=5 mm//s`.
Hence `tantheta=|(v_(iy))/u_(ix)|=(5)/(5sqrt3//2)=(2)/(sqrt3) and v_(i)=sqrt(((5sqrt3)/(2))^(2)+(5)^(2))=(5sqrt 7)/(2)mm/s`