A driver having a definite reaction time is capable of stopping his car over a distance of 30 m on seeing a red traffic signal, when the speed of the car is 72 km/hr andover a distance of 10 m when the speed is 36 km/hr. Find the distance over which he can stop the car if it were running at a speed of 54 km/hr. Assume that his reaction time and the deceleration of the car remains same in all the three cases.

Options

A. 30 cm towards the mirror
B. 36 cm away from the mirror
C. 30 cm away from the mirror
D. 36 cm towards the mirror

Answer

B

Explanation

Key concept The net displacement of the images is equal to the difference between the image distances in both the cases.
case 1 When the object distance, `u_(1) = -40cm`
Focal length of mirror, `f=-15cm`

Using the mirror formula, we get
`1/f = 1/v_(1) +1/u_(1)`
Substituting the given values, we get
`-1/15 = 1/v_(1)+ (-1/40)`
`rArr 1/v_(1) = 1/40 -1/15 = (3-8)/(120)=-5/120)`
`rArr v_(1)= (-120)/5 = -24cm`
Case 2 When the object distance, `u_(2)=20cm`

using the mirror formula, we get
`1/f = 1/v_(2)+1/u_(2)`
substituting the given values, we get
`-1/15 = 1/v_(2) + (-1/20)`
`rArr 1/v_(2)=1/20-1/15=(3-4)/60 = -1/60`
`rArr v_(2) = -60cm`
`therefore` The displacement of the image is
`=v_(2)-v_(1) = -60-(-24)=-60+24`
or `=-36 cm`
= 36 cm, away from the mirror