Question

On a foggy day two drivers spot each other when they are just 80 metres apart. they are travelling at 72km/h and 60km/h respectively. both of them applied brakes retarding their cars at a rate of 5m/s^2. determine whether they avert collision or not.

Answer 1

s=80m
v1=72*5/18=20m/s
just like that
v2=50/3m/s
so velocity of v1 with respect to v2=20+50/3
=110/3 m/s
a1=-5m/s^2=a2
so retardation with respect to other=5+5=10m/s^2
so s=(v^2-u^2)/2a
=0-(110/3)^2/(-2*10)
1210/18=67.22m
so 67.22<80 m
so collision won't take place.

Answer 2

Given:

Speed of first car = 72 Kmph = 72000 m/60*60 = 72000/3600 = 20m/s

Rate of retardation = -5 $m/s^2$

Wkt,

                                     $v^2 -u^2 = 2as$

Initial velocity = 0

                                $0^2 -(20)^2 = 2 (-5) s$

                                             0 – 400 = -10s

                                                S = 400/10 = 40m

It will stop after travelling 40m

Similarly for second car, speed = 60 kmph = 60000/60*60 = 16.667 m/s

Rate of retardation = -5 m/s2

Wkt,

                                        $v^2 -u^2 = 2as$

Initial velocity = 0

                             $0^2 -(16.67)^2 = 2 (-5) s$

                                          0 – 277.89 = -10s

                                                         S = 27.79m

The second car will stop after travelling 27.79 m

The sum of their distances = 40+ 27.79 = 67.79m which is less than the total distance between them that is 80 m

Hence no collision will occur.