1) Your driving your car at 15.6 ms-1 (about 35 mph) and the traffic light ahead turns amber. Do you brake before the intersection or hit the gas pedal and beat the light? The light has a speed camera which will automatically deposit a hefty fine in the mail (along with a picture of your car speeding through the intersection or stopping within the intersection) if you get it wrong.
The traffic light will remain amber for 3.5 seconds (Texas state minimum), your reaction time is 0.75 s and the intersection is 10 m wide. When you first saw the light turn amber, you where 40 m in front of the intersection. Your car can accelerate at a rate of 4 m s-2 or decelerate at a rate of 6 m s -2.
In Dallas a speed camera issued 9407 tickets worth $705,525 between January 1 and August 31, 2007. Upon investigation by a local news station it was found that the amber light lasted only 3.15 s. How might the decision of the corrupt local government in Dallas, to put profit before safety and reduce the length of time for the amber light, affect your above predicament?
i. The first part is to consider the car approaching the intersection with a 3.5 s amber light. What would happen if you decided to just continue at the same speed through the intersection? What deceleration would the car require to stop in time? What acceleration would the car require to clear the intersection before the light turns red? Don't forget to include the reaction time in your calculations. Are these values reasonable?
ii. Repeat the same analysis as in part i but with the time that the amber light is on at 3.15 s instead of 3.5 s. How does this change your answers?
2) The chef on the Titanic, Charles Joughin, helped many people onto lifeboats and declined to board one himself. Subsequent to helping others he drank an entire bottle of whiskey, put on a life jacket and, after the Titanic had completely been submerged, stepped onto the bow of the ship without as much as getting his hair wet. Both the alcohol (kept him warm) and the life jacket (kept him afloat) saved his life. His mass was 100 kg and the inflated jacket had a volume of 3.1 x 10-2 cubic meters and was completely submerged under the water. The volume of the chef's body that was underwater is 8.2 x 10-2 cubic meters.
What was the density of the life jacket?
This question has a lot of unrequired information, which I think makes it interesting. The relevant part is that the chef was floating in water and kept afloat by the life jacket. A FBD of this situation would see the weight of the chef and life jacket (mass is density multiplied by volume) being equal to the buoyant forces (weight of water displaced). I believe the only unknown (after taking the density of water to be 1000 kg m-3, will be the density of the life jacket.