Monica is hurrying off to her physics class, jogging down the sidewalk at a spee

Question

Monica is hurrying off to her physics class, jogging down the sidewalk at a speed of 3.80m/s . Her friend Manny 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 50.8m above the street level and directly above the sidewalk, to throw them to her. Manny throws them horizontally at a time 4.50s after Monica has passed below the window, and she catches them on the run. You can ignore air resistance.

Part A)

With what initial speed must Manny throw the bagels so Monica can catch them just before they hit the ground?

Hint: The bagels move along a projectile trajectory. Find Monica's location when the bagels reach the ground and demand that the bagels have this same range. When the bagels reach the ground, y_final=0m, and they start at y_initial at hieght of window. Since v_initial has only an x-component, it is straightforward to calculate the time that they will be in the air. You have to add that time onto the jog time.

Part B)

Where is Henrietta when she catches the bagels?

Explanation / Answer

Time to drop 50.8 metres = sqrt.(2h/g) = 3.2198 secs. (9.8 = g)

In this time, Monica will be (4.5 + 3.2198) = 7.7198 secs. past the window.

(7.7198 x 3.80) = 29.33 m. from below the window.

a) Horizontal velocity required = (29.33/3.2198) = 9.110 m/sec. Ans.

b) If Henrietta is Monica, she is 29.33 m. from below the window. Ans.

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