Evil forces have compelled you to throw water balloons off of the roof of your a

Question

Evil forces have compelled you to throw water balloons off of the roof of your apartment building (which is 12-m high) in what you claim are random directions. One particularly random toss of a balloon results in the balloon leaving your hand with an initial speed vi at an angle of 27 above the horizontal. This balloon just happens to hit little Fern Hugo-Martinez, a geeky pencil-necked twerp who you just-so happen to particularly detest, right on the ole bean (his head!). Fern is sitting on the ground a distance D from the base of your building when he is randomly and accidentally hit by your wayward balloon, 1.7 s after you threw it. (a) What was the value of the speed vi with which you threw the balloon? (b) What was the distance D that Fern was sitting from the base of your building? (c) What was the velocity of the balloon just before it hit poor little Fern’s head?

Explanation / Answer

along vertical

viy = vi*sin27

ay = -g = -9.8 m/s^2

y = -12 m

from equations of motion

y = viy*T + 0.5*ay*T^2

12 = vi*sin27*1.7 - 4.9*1.7^2

vi = 33.897 = 34 m/s(nearly)

part(b)

along horizantal

vix = vi*cos27

ax = 0

x = D

therefore from equations of motion

x = vix*T + 0.5*ax*T^2

D = vi*cos27*1.7 = 34*cos27*1.7 = 51.5 m <-----answer

---------------

part(c)

vfx = vix + ax*T = vix = 34*cos27 = 30.294 m/s

vfy = voy + ay*T

Vfy = (34*sin27)-(9.8*1.7) = -1.224 m/s

Vf = sqrt(vfx^2+vfy^2) = 30.319 m/s

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