# Annoying juggler problem

#### DB

a juggler performs in a room whose ceiling is 3 m above the level of his hands. he throws a ball vertically upward so that it JUST reaches the ceiling. he then throws a second ball upward with the same inital velocity, at the instant the first ball is at the ceiling. How long after the second ball is thrown do the two balls pass each other?

okay, so i've gotten that the intial velocity of the balls is 7.75 m/s and that the time required for a ball to hit the ceiling is 0.775 seconds. the answer sheet tells me this is right. so i thought that, considering the situation, the balls would pass eachother halfway through their trips, at 1.5 m. so i solved the quadratic that gave me how long it would take the second ball to reach 1.5 m and i got 0.175 seconds. this is wrong. how come? if they dont pass each other halfway through their trips then when?

#### Aneleh

You're trying to solve for when they pass each other, you can't just guess (well you can but...) at 1.5m they pass. If you imagine the paths followed by the two balls and you want to find the point where they have the same height, use your quadratic equations for both balls by equating the height, then solve for the time.

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