Question

February 3, 2009, was a very snowy day along Interstate 69 just outside of Indianapolis, Indiana. As a result of the slippery conditions and low visibility (50 yards or less), there was an enormous accident involving approximately 30 vehicles, including cars, tractor-trailers, and even a fire truck. Many witnesses said that people were driving too fast for the conditions and were too close together. In this problem, we explore two rules of thumb for driving in such conditions. The first is to drive at a speed that is half of what it would be in ideal conditions. The other is the "8-second" rule: Watch the vehicle in front of you as it passes some object such as a street sign, and you should pass that same object 8 seconds later. On a dry road, the 8-second rule is replaced by a 3-second rule.

a.  Assume vehicles on a slippery interstate highway follow both rules. What is the distance between the vehicles?

b. If a driver followed the first rule of thumb, driving at a lower speed, but used the 3-second rule instead of the 8-second rule, what is the distance between the vehicles?

c. Suppose drivers do not follow either rule of thumb for slippery conditions. What is the distance between vehicles?

d. Suppose a driver was not obeying either rule of thumb when she sees a tractor-trailer that stopped on the highway. She presses on her brakes, locking the wheels, and her car crashes into the truck. Estimate the magnitude of the impulse exerted on her car. (Give the impulse exerted on the car by the tractor-trailer. Assume the coefficient of kinetic friction between rubber and ice is 0.15. Assume an instantaneous reaction time.)

e. Calculate the impulse on the car in part (d) had the driver followed both rules of thumb for slippery conditions instead of ignoring them. (Give the impulse exerted on the car by the tractor-trailer. Assume an instantaneous reaction time.)

I'm using a 1000kg car that would be driving 30 m/s in ideal conditions. I've gotten all but 'e' correct. These were my answers:

a: 120 m

b: 45 m

c: 90 m

d: 27792.75 N/s

e: ???

Answer 1