In the annual battle of the dorms, students gather on the roofs of Jackson and W

Question

In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 36.5 m, and the heights of the Jackson and Walton buildings are, respectively, 16.0 m and 24.0 m. Ignore air resistance.
(a) The first balloon launched by the Jackson team hits Walton dorm 1.9 s after launch, striking it halfway between the ground floor and the roof. Find the direction of the balloon's initial velocity. Give your answer as an angle measured above the horizontal.
____ °

(b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.
____ m/s

Explanation / Answer

a)The equations of motion of J's ballon:

x = ucos(theta)*t

-y = usin(theta)*t-0.5gt^2

u is the initial velocity

theta is the angle of projection

the horizontal distance travelled by the balloon 36.5 m = ucos(theta)*t

The vertical distance travelled by the ballon -(16-24/2)m = usin(theta)*t-0.5gt^2

-4m+0.5gt^2 = usin(theta)*t

[usin(theta)*t]/[ucos(theta)*t] = [-4 m+0.5gt^2]/[36.5 m]

tan(theta) = 0.3755

theta = 20.58 degree above the horizontal

b)

As the second balloon hits the roof of W's building

The horizontal displacement of the balloon 36.5 m = u*cos20.58*1.9

                                                                   u = 20.52 m/s

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