George is driving 100 ft/sec toward an intersection.
He looks to his right, and sees Bill, driving 30 ft/sec toward the same intersection. George foolishly slams on his brakes.

If he had kept going 100 ft/sec, he would have been through the intersection long before Bill got there.

At the instant that he slams on his brakes, the center of George's car is 125 ft from the intersection, and the center of Bill's car is 150 ft from the intersection. George's brakes give his car an acceleration of -30 ft/sec².
Bill never changes his speed.
Each car is 13 ft long and 7 ft wide.

Will there be a collision?

I know it's been discussed a lot, and the fact that George comes to a stop at 3.33 seconds has been pointed out. But it's been bugging me that the rest of the problem didn't get formally solved, so here it is.

To find out how long it takes George to stop:
V = 0 = 100ft/s + (-30ft/s/s)*T
T = 10/3 seconds = 3.3333 seconds

Now, let's see how far the center of George's car travelled from when he hit the brakes and when he stopped:
Dg = 100ft/s * 10/3s + 0.5*(-30ft/s/s)*(10/3s)^2
Dg = 166.666 ft

And let's see how far the center of Bill's car travelled during this time:
Db = 30ft/s * 10/3s
Db = 100ft

So at the moment George stopped, he has already passed through the intersection, and the back end of his car is 35.16ft from the center of the intersection. Bill hasn't gone through the intersection yet, and the front end of his car is 43.5ft from the center of the intersection.

Both of these numbers show that there is enough clearance for these 13x7 cars to avoid a collision.

Posted by nikki on 2003-10-02 16:15:00