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?

(In reply to fiziks...here goes by Vito)

You almost had the right answer, but dismissed the wrong value of t. At t=1.667s George is busy sliding through the junction (forwards). At t=3.333s George is at a standstill. Continuing to apply a deceleration of -30f/s/s means that at t=5 he is travelling backwards through the junction.

Looking at the problem with simple sums (ie no calculus)...

George's car comes to a halt at 3.333s (=100/30)
Over those 3.333s George's average velocity was 50f/s (=100/2), which means that he travelled 166.667 ft ie over 40 ft past the junction.
After 3.333s Bill has travelled 100ft, so he still has 50ft to travel before he gets to the junction.
Even allowing for the lengths and widths of the cars there is no collision before or at 3.333s. There is also no collision at any time after 3.333s since George is at a standstill sufficiently far through the junction that Bill doesn't hit him.

Posted by fwaff on 2003-10-03 04:22:47