Harold, a menacing young boy, shoots his pellet gun at a pigeon from his penthou

Question

Harold, a menacing young boy, shoots his pellet gun at a pigeon from his penthouse apartment window. A kind old lady, Mrs. Chenshaw, had exited the apartment building earlier and was 131 m from the base of the building at the instant when Harold fired his shot and was walking away from the building at a constant speed of 1.40 m/s. Harold's apartment window is 158 m from the ground, the muzzle velocity of Harold's pellet gun is 51.5 m/s, and Harold shot at the pigeon with a 74.6o angle above hortizontal. Harold's shot missed the pigeon and was, unfortunately, hortizontally aligned with Mrs. Crenshaw's direction of travel. When Harold's shot strikes the ground, does it fall short or travel beyond Mrs. Crenshaw?_______________ Where does the shot land relative to the kind old woman (positive distance= beyond her, negative distances=behind her)?____________m. How much time elapses between the time the shot was fired and when it hits the ground?__________seconds

Explanation / Answer

to reach the ground,

vertical dispalcement, y = 0 - 158 = - 158 m

initial vertical velocity, v0y = 51.5 sin74.6 = 49.6 m/s

ay = - 9.8 m/s^2

Applying y = v0y t + ay t^2 / 2

- 158 = 49.6t - 4.9 t^2

4.9 t^2 - 49.6t - 158 = 0 ]

t = 12.7 sec

horizontal distance covered by pellet = (51.5 cos74.6) (12.7)

x = 173.7 m

distance covered by Chensaw in this time = 1.40 x 12.7 = 17.8 m

distance of Chensaw from base of building = 17.8 + 131 = 148.8 m

1. It travel beyond the Mrs. Chensaw

2. d = 173.7 - 148.8 = 25 m

3. t = 12.7 sec

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