Henrietta is going off to her physics class, jogging down the sidewalk at a speed of 4.20 m/sm/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 52.9 mm above the street level and directly above the sidewalk, to throw them to her. Bruce throws them horizontally at a time 4.50 ss after Henrietta has passed below the window, and she catches them on the run. You can ignore air resistance. Required:
a. With what initial speed must Bruce throw the bagels so Henrietta can catch them just before they hit the ground?
b. Where is Henrietta when she catches the bagels?

a)  v₀ₓ = 9.9 m / s, b)  x_woman = 32.7 m

Explanation:

A) In this exercise, the movement of the bagels is parabolic, we find the time it takes to reach the floor.

          y = y₀ + v_{oy} t - ½ g t²

          0 = y₀ + 0 - ½ gt²

          t =

let's calculate

          t =

          t = 3,286 s

Now we can analyze how long Henrieta has walked, she has a walking time before the bagel movement begins (t₀ = 4.50 s)

          t_woman = t₀ + t

           t_woman = 4.50 + 3.286

           t_woman = 7.786 s

The distance traveled in this time is

           x_{woman} = v_woman t_woman

            x_{woman} = 4.20 7.786

          x_{woman} = 32.7 m

For her to grab the bagel, the two of them must be at this point

          x_bagel = x_woman

          x_bael = vox t

          v₀ₓ = x_bagel / t

          v₀ₓ = 32.7 / 3,286

           v₀ₓ = 9.9 m / s

b) when catching the bagels this point x_woman = 32.7 m

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min