xmPuzzle 010: Time of flight

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A bio teacher , chem teacher and physics teacher were having a nice chat when the bio cher suddenly went ballistic. Being omnidextrous, the bio cher threw 2 mugs at the same instant. The trajectories of the projectiles are shown in the diagram. Being equally retarded, the chem and physics chers started taking evasive action the same split second after the projectiles were launched. One teacher a bruised forehead. Which one?

THIS IS A WORK OF FICTION. NAMES, CHARACTERS, BUSINESSES, PLACES, EVENTS, LOCALES, AND INCIDENTS ARE EITHER THE PRODUCTS OF THE AUTHOR’S IMAGINATION OR USED IN A FICTITIOUS MANNER. ANY RESEMBLANCE TO ACTUAL PERSONS, LIVING OR DEAD, OR ACTUAL EVENTS IS PURELY COINCIDENTAL.

 

Answer:

The physics teacher got hit.

In a projectile motion, the initial vertical velocity decides (1) the maximum height H (think 02 = uy2 – 2gH) and (2) the time of flight tflight (think tpeak = uy/g and tflight = 2tpeak)

The fact that the projectile aimed at the chemistry teacher reaches a higher maximum height implies that its time of flight is longer. So the chemistry teacher could dodge in time.

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