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On a foggy day two drivers spot each oth...

On a foggy day two drivers spot each other when they are just 80 meters apart. They are travelling at `27kmh^(-1)` and `60kmh^(-1)` , respectively. Both of them applied brakes retarding their cars at the rate of `5ms^(-1)` Determine whether they avert collision or not.

Text Solution

Verified by Experts

The correct Answer is:
`67.78`
For the first car
`u = 72 kmh^(-1) = 20 ms^(-1) , v= 0 , a = -5 ms^(-2)`
As `v^(2) -u^(2) = 2as`
`rArr 0^(2) - 20^(2) = 2 (-5)s_(1)`
` :. ` Distance covered by first car , `s_(1) = 40 m `
For the second car ,
` u = 60 kmh^(-1) = (60 xx 5)/18 = 50/2 ms^(-1)`
v =0 , `a= -5 ms^(-2)`
As `v^(2) - u^(2) = 2as`
` :. 0^(2) = (50/3)^(2) = 2 (-5)s_(2)`
Distance covered by second car ,
`s_(2) = 2500/(9 xx 10) = 27.78 m ` .
Total distance covered by the two cars .
`= s_(1) +s_(2) = 40 + 27.78 = 67.78 m `
Note : As this distanc is less than the initial distance (=80 m) between the two cars , so the collision will be averted .
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