Weekly Physics Problem Contest
Summer 2015
Correctly solve the problem stated below showing all necessary calculations and submit your solution to Dr. Jaquin before the deadline. A winning submission will be chosen based on correctness, completeness, elegance and neatness of the submitted solution. The winner will be awarded a coupon for a free Jreck sub, side and drink redeemable at the Jreck Sub shop at the corner of Valley Drive and Seneca Turnpike.
The Problem
The IRTAP Bank (Insanely Rich from Taking Advantage of the Poor) is transporting via railroad 1 Pentillion (1015) dollars in gold bullion. Needless to say the train is very well guarded. Hijacking the whole train is not possible. However, you and your band of merry men have a plan to sever the train just in front of the Cash Car and hijacking just that car with a high speed engine that is following at a discrete distance. The success of the heist depends on your technical team that has to launch a small explosive charge from a bridge as the Cash Car passes under it. The charge is fired from a motor-like device and must pass between the roofs of the Cash Car and the Guard Car in front of it, not touching either car, detonating as it impacts the car coupling mechanism. Once the Cash Car is severed, the high speed engine in hiding hooks up to the rear of the Cash Car, decelerates it and makes it’s get away in the opposite direction. Once you and your men obtain the gold, you plan on distributing it to small banks throughout the third world for low cost loans to small local businesses independent of the borrower’s age, race, religion or gender. See figure below.
You as the Technical Team Leader must calculate the angle and speed at which the charge leaves the mortar-like firing device. You have the following facts:
Speed of train = 75 km/hr
Height of train car roof above the track = 6.5 m
Height of train car coupling above the track = 1.2 m
Horizontal space between the adjacent train car roof’s = 2.0 m
Height of firing device above the track = 15 m
What firing angle and muzzle velocity will land the charge on the coupling without hitting either car? When should the charge be fired relative to the time the Crash Car coupling passes under firing device on the bridge?
Algebraic solutions are preferred over numerical solutions. Solutions due by next Monday night to Dr. Jaquin by hand or email.