91Ó°ÊÓ

The velocity contains two components, one is horizontal component and another one is vertical.

According to the newton’s laws of motion,

$s=ut+\frac{1}{2}a{t}^2$

Where, s, u, t, a, are displacement, initial velocity, time, and acceleration.

For the vertical and horizontal motion, the velocity component will be respectively.

Henrietta jogging speed = 3.05m/s

Window vertical distance from the street = 38.0m

Passed time = 9.0s

The initial velocity is zero, so from the vertical motion equation,

$$\begin{gathered} \mathrm{s}=\frac{1}{2}{\mathrm{gt}}^2 \\ 38.0\mathrm{m}=\frac{1}{2}\left(9.8\mathrm{m}/{\mathrm{s}}^2\right){\mathrm{t}}^2 \\ \mathrm{t}=2.78\mathrm{s} \end{gathered}$$

So she has been jogging for

$9.00\mathrm{s}+2.78\mathrm{s}=11.78\mathrm{s}$

The horizontal distance with this time she travels is,

$$\begin{gathered} s=ut \\ s=\left(3.05m/s\right)\left(11.78s\right) \\ s=35.09m \end{gathered}$$

Bruce must throw the bagels so they travel horizontally about 35.9m in the time period of 2.78s. Now from the Newton’s law,

$$\begin{gathered} s=ut \\ 35.9m=u\left(2.78s\right) \\ u=12.9m/s \end{gathered}$$

Henrietta is at 35.9m distance from the building when she catches the bagels.