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SERPSE$1028\mathrm{.}4.$OP$\mathrm{.}017.$CTX$.$

You are working during the summer at a company that builds theme parks. The company is designing an electromagnetic propulsion system for a new roller coaster. A model of a substructure of the device appears in the figure below.

The rod is of length $d=1\mathrm{.}00m$ and mass $m=0\mathrm{.}600kg.$ The rod carries a current $I=100A$ in the direction shown and rolls along the rails of length $L=20\mathrm{.}0m$ without slipping. The entire system of rod and rails is immersed in a uniform downward$-$directed magnetic field with magnitude $B=2\mathrm{.}40T.$ The electromagnetic force on the rod is parallel to the rails, causing the rod to roll to the right in the figure. When a full$-$scale device is produced, this rod will represent the axle of wheels on which the car and its passengers ride. The electromagnetic force on the axle will provide the motion of the car at the beginning of the roller$-$coaster ride. Your supervisor wants to test the substructure in the figure in a flat outdoor area on the grounds of the company. By projecting the rod from the rails in a horizontal direction from a height $h=2\mathrm{.}40m,$ the projection speed can be determined from how far from the ends of the rails the rod hits the ground. Your supervisor asks you to determine the length of the outdoor area needed to test the device. $($Determine the total horizontal distance, in m $,$ from the initial position of the rod on the tracks to the final position of the rod where it lands on the ground.$)$

Use energy considerations to find the speed with which the rod reaches the end of the rails. Then, treat the rod as a projectile. m

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