In the annual battle of the dorms, students gather on the roofsof Jackson and Wa

Question

In the annual battle of the dorms, students gather on the roofsof Jackson and Walton dorms to launch water balloons at each otherwith slingshots. The horizontal distance between the buildings is37.0 m, and the heights of the Jackson and Walton buildings are,respectively, 15.0 m and 22.0 m. The first balloon launched y theJackson team hits Walton dorm 1.90 s after launch, striking ithalfway between the ground and the roof. Ignore air resistance.(a) Find the direction of the balloon's initialvelocity. Give your answer as an angle (in degrees) measured abovethe horizontal. (b) A second balloon launched atthe same angle hits the edge of Walton's roof. Find the initialspeed of this second balloon.

Explanation / Answer

(a)the maximum height reached by the first balloon is h =(1/2)H the horizontal range of the first balloon is R H = (u2 * sin2/2g) and R = (u2 * sin(2)/g) h = (1/2) * (u2 * sin2/2g) =(u2 * sin2/4g) (h/R) = ((u2 *sin2/4g)/(u2 * sin(2)/g)) = (1/8)* tan or = tan-1(8h/R) ----------(1) h = (1/2)H = (1/2) * 15.0 = 7.5 m R = 37.0 m the direction of the balloon's initial velocity is given byequation (1) (b)let the initial speed of the second ballon bevo' therefore we get H = (vo'2 *sin2/2g) or vo' = (2gH/sin2)1/2= [(2gH)1/2/sin] g = 9.8 m/s2 and the angle is given byequation (1)

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