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 33.5 m, and the heights of the Jackson and Walton buildings are, respectively, 14.5 m and 21.0 m. Ignore air resistance.
(a) The first balloon launched by the Jackson team hits Walton dorm 2.2 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

d = 33.5 m, hJ = 14.5 m, hW = 21.0 m.
(a) t = 2.2 s,

vertical displacement y = hW/2 - hJ = -4.0 m (upward is positive direction)

d = vxt, so vx = d/t = 15.2 m/s

y = vyt - gt2/2, so vy = y/t + gt/2 = 8.96 m/s

v = (vx2 + vy2) = 17.6 m/s

angle = tan-1(8.96/15.2) = 30.5°

(b) Find the initial speed of this second balloon u. (time = t')

d = ucos*t', so t' = d/(ucos)

y = hW - hJ = 6.5 m = usin*t' - gt'2/2 = dtan - gd2/(2u2cos2)

6.5 = 33.2*tan(30.5) - 9.81*33.52/[2u2cos2(30.5)]

u = 23.8 m/s

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.