With what initial speed must Bruce throw the bagels so Henrietta can catch them jus before they hit the ground

Question

Tossing Your Lunch. Henrietta is going off to her physics class, jogging down the sidewalk at a speed of v. 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 h above the street level and directly above the sidewalk, to throw them to her. Bruce throws them horizontally at a time t 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?
Take free fall acceleration to be g.

Where is Henrietta when she catches the bagels?
Take free fall acceleration to be g.

i know how to do it when there is actual values, but in this case it is all symbolic so im struggling to achieve correct answer.

Best i could do is: V(t+sqrt2h/g) all divided by t

wrong tho, help please, if someone could explain the method needed

Answer 1

Calculate time of drop:

T= square root of [h/4.9]

Calculate horizontal distance Henrietta will be when she catches them:

(t+T)v [time she has already spent plus the time it takes the bagels to drop].

Divide to find necessary horizontal velocity.

Answer 2

I'm not sure I understand the question, but let's see what I can do for you anyway.

If the bagels are thrown horizontally, you know their initial vertical velocity is 0. You also know the acceleration due to gravity. So you can use the distance equation for motion under constant acceleration:

D = Vi x T + (1/2) x A x T^2

to compute the bagel flight time, T.

So where will Henrietta be at time T after Bruce throws the bagels? That gives the horizontal distance the bagels have to travel.

The minimum horizontal velocity of the bagels is distance/time, where

distance is from the point under the window to where Henrietta will be when the bagels arrive

time is the bagel traveling time or T.