A man running at a speed of 5m/s is viewed in the side view mirror of radius of curvature R is 2m of a stationary car. Calculate the speed of image when the man is at a distance of 9m from the mirror.?

Question

Answer

Given information:
- Speed of the man, v = 5 m/s
- Radius of curvature of the side view mirror, R = 2 m
- Distance of the man from the mirror, d = 9 m

Calculating the focal length:
The focal length of a mirror can be calculated using the formula:

1/f = 1/R

Where f is the focal length of the mirror. Substituting the given value of R, we get:

1/f = 1/2
f = 2 m

Calculating the distance of the object from the mirror:
The distance of the object from the mirror (u) can be calculated using the formula:

1/f = 1/u + 1/v

Substituting the given values of f and v, we get:

1/2 = 1/u + 1/5
1/u = 1/2 - 1/5
1/u = (5 - 2)/10
1/u = 3/10
u = 10/3 m

Calculating the distance of the image from the mirror:
The distance of the image from the mirror (v') can be calculated using the formula:

1/v' = 1/f - 1/u

Substituting the values of f and u, we get:

1/v' = 1/2 - 1/(10/3)
1/v' = 1/2 - 3/10
1/v' = (5 - 3)/10
1/v' = 2/10
v' = 10/2
v' = 5 m

Calculating the speed of the image:
The speed of the image can be calculated using the formula:

v'/v = u/(u - d)

Substituting the given values of u and d, we get:

v'/5 = (10/3)/(10/3 - 9)
v'/5 = (10/3)/(10/3 - 27/3)
v'/5 = (10/3)/(10 - 27)/3)
v'/5 = (10/3)/(-17/3)
v'/5 = -10/17
v' = -50/17 m/s

Therefore, the speed of the image when the man is at a distance of 9 m from the mirror is approximately -2.94 m/s.

Answer

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