Question

A motorcyclist observes a car coming from behind with a diminished 1/6. If the actual distance between the car and the bike is 30 m calculate the radius of curvature of the mirror.​

Answer 1

Explanation:

a car coming from behind with a diminished 1/6. If the actual distance between the car and the bike is 30 m calculate the radius of curvature of

Answer 2

$\mathfrak{\bf{\underline{\underline{Given :- }}}}$

⟹ u = -30 m

⟹ v = ?

$\implies \mathsf{m \: = + \frac{1}{6} }$

$\mathfrak{\bf{\underline{\underline{Formulaes \ used :- }}}}$

$\star \: \: \mathsf{m = \frac{ - v}{u} }$

$\star \: \: \mathsf {f = \frac{uv}{u + v} }$

$\star \: \: \mathsf {R=2f }$

$\mathfrak{\bf{\underline{\underline{To \ Find :- }}}}$Radius Of Curvature of Mirror.

$\mathfrak{\bf{\underline{\underline{Solution :- }}}}$

$\implies \mathsf{m = \frac{ - v}{u} = + \frac{ 1}{6} }$

$\implies \mathsf{ \frac{ - v}{30} = \frac{1}{6} }$

$\implies \: \mathsf{v = - 5m}$

$\mathsf{\star \: Note : \: distance \: can \: never \: negative}$

$\therefore \: \mathsf{v = 5m}$

Now ,

$\implies \: \mathsf {f = \frac{uv}{u + v} }$

$\implies \mathsf{ f = \frac{ - 30 \times 5 }{ - 30 + 5} }$

$\implies \mathsf{ f = \frac{ - 150 }{ - 25} }$

$\implies \mathsf{ f = 6m }$

$\implies \mathsf{ R=2f }$

$\implies \mathsf{ f = 6m }$

$\implies \mathsf{ R = 2 × 6 = 12m }$

ㅤㅤㅤ★$\boxed{\mathsf{\red{ R = 12m }}}$★

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