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 36.0 m, and the heights of the Jackson and Walton buildings are, respectively, 14.0 m and 24.0 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.

Explanation / Answer

The horizontal distance between the buildings

R = 37.0 m
The height of J building is h = 17 m

The height of W building is H = 22 m

The time of flight of the balloon T = 2 s

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 37 m = ucos(theta)*t

Thevertical distance travelled by the ballon

-(17-22/2)m = usin(theta)*t-0.5gt^2

-2.5 m+0.5gt^2 = usin(theta)*t

[usin(theta)*t]/[ucos(theta)*t] = [-2.5 m+0.5gt^2]/[35 m]

tan(theta) = 0.36397023426

theta = 20 degree above the horizontal

b)

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

Thehorizontal displacement of the balloon 37 m

= u*cos20*2

u = 29 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.