With what initial speed must Bruce throw the bagels so Henrietta can catch them

Question

With what initial speed must Bruce throw the bagels so Henrietta can catch them just before they hit the ground?
Where is Henrietta when she catches the bagels? Henrietta is going off to her physics class, jogging down the sidewalk at a speed of 3.43m/s . Her husband Bruce suddenly realizes that she left in such a hurry that she forgot her lunch of bagels, so he runs to the window of their apartment, which is a height 42.3m above the street level and directly above the sidewalk, to throw them to her. Bruce throws them horizontally at a time 5.5s after Henrietta has passed below the window, and she catches them on the run. You can ignore air resistance. With what initial speed must Bruce throw the bagels so Henrietta can catch them just before they hit the ground? Where is Henrietta when she catches the bagels?

Explanation / Answer

Let the initial velocity of the object is u m/s,Let the object take t sec to fall the vertical distance i.e. 42.3 m,
=>By s = ut + 1/2gt^2
=>42.3 = 0 + 1/2 x 9.8 x t^2
=>t = sqrt[8.63]
=>t = 2.93 sec
=>The distance traveled by object in t sec = The distance traveled by Henrietta in (t+5.50)
=>u x 2.93 = 3.43 x (2.93+5.50)
=>u = 9.86 m/s
2) Distance traveled by Henrietta = 3.43 x (2.93+5.50) = 28.9149 m
All data provided by you is supposed to be in SI unit.

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