posted by John on .
The car in front of you is driving 105 km/h on the highway. You pull out to pass the car travelling 114 km/h. Both cars are 2.7m long. You pull out when you are 10m behind the car in front of you and pull back in when you are 10m in front of the other car. How long does it take you to pass the car? How far did you travel?
In relative distance, you travel 2.7x2 meters. Your relative velocity is 9km/hr (change to m/s).
time to pass: relative distance/relative speed
Now, with that time; how far did you travel..
RELATIVE DISTANCE IS 5.4 METERS
(VELOCITY=SPEED)TO FIND RELATIVE SPEED IN M/S, WE DO THAT A.T.Q.
9*1000/60*60=9000/3600=5/2 =2.5 M/S
TIME TO PASS =5.4/2.5=2.16
DISTANCE =2.5*2.16 =5.4 METERS
Actually, the two people above are wrong. They did not take into account the 10m travelled behind and in front. The total distance is 25.54 m (10+2.7+10+2.7). The velocity relative to the other car is 9km/h (2.5 m/s). You must use 9 km/h and not 114 km/h because the other car is in motion too. Thus the time is 25.54/2.5, which is 10.16 s. With significant digits, the answer is 10 seconds.