a) calculate the time of flight of the water balloon b) determine the velocity o

Question

a) calculate the time of flight of the water balloon
b) determine the velocity of the water balloon just before it strikes the roof of the nearby building
c) find the horizontal distance the balloon travels after release

Test I Page 2 Problem (20 points) 22.5 ms A prankster theows a wster balloos off the top of a 3038 m m high building downward to the roofofnearly 38 m high building, The little urchin launches the water bualloon with a speed of 22.3 m/s at an angle of 4 below the horizcatal. A) Calculate the time of flight of the water balloon. B) Determine the velocity of the water balloon just before it strikes the roof of the nea building. C) Find the horizontal distance the balloon travels after release

Explanation / Answer

a)

Vi = initial velocity of launch = 22.5 m/s

Viy = intial velocity in y-direction = Vi Sin40 = 22.5 Sin40 = 14.5 m/s

Vix = intial velocity in x-direction = Vi Cos40 = 22.5 Sin40 = 17.2 m/s

dy = vertical displacement = 50 m - 38 m = 12 m

ay = acceleration in Y-direction = 9.8 m/s2

t = time taken

Along the Y-direction ::

Using the equation

dy = Viy t + (0.5) ay t2

12 = (14.5) t + (0.5) (9.8) t2

t = 0.67 sec

b)

Along Y-direction :

Using the equation :

Vfy = Viy + ay t

Vfy = 14.5 + (9.8) (0.67)

Vfy = 21.1 m/s

we know along X-direction , the velocity does not change since there is no acceleration

so Vfx = Vix = 17.2 m/s

net velocity is given as ::

Vf = sqrt(V2fy + V2fx )

Vf = sqrt (21.12+ 17.22)

Vf = 27.2 m/s

c)

horizontal distance travelled can be given as ::

dx = Vix t

dx = 17.2 x 0.67

dx = 11.52 m

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