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, 14.5 m and 21.5 m. Ignore air resistance.

(a) The first balloon launched by the Jackson team hits Walton dorm 1.8 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.

To find the direction of the balloon's initial velocity, we can use the principles of projectile motion.

First, let's define the given information:
Horizontal distance between the buildings (d): 36.0 m
Height of Jackson dorm (h_j): 14.5 m
Height of Walton dorm (h_w): 21.5 m
Time taken for the balloon to reach Walton dorm (t): 1.8 s

To solve this problem, we can break it into two components: horizontal and vertical.

1. Horizontal Component:
The horizontal component of velocity remains constant throughout the motion.
Let's assume the initial velocity of the balloon in the horizontal direction is (v_x).

The horizontal distance traveled by the balloon is given by:
d = v_x * t

From the given information, we know:
d = 36.0 m,
t = 1.8 s

By substituting these values, we can find the horizontal component of velocity:
v_x = d / t

2. Vertical Component:
The vertical component of velocity changes due to the force of gravity acting on the balloon.
Considering the midpoint between the ground floor and the roof of Walton dorm, the vertical displacement (y) is given by:
y = (h_w - h_j) / 2

From the given information, we know:
h_w = 21.5 m,
h_j = 14.5 m

By substituting these values, we can find the vertical displacement:
y = (21.5 m - 14.5 m) / 2

Now, we can use the equations of projectile motion to find the magnitude and direction of the balloon's initial velocity.

The magnitude of the initial velocity is given by:
v = √(v_x^2 + v_y^2)

The direction of the initial velocity is given by the angle (θ) measured above the horizontal:
θ = arctan(v_y / v_x)

By substituting the calculated values of v_x and v_y into these equations, we can find the magnitude and direction of the balloon's initial velocity.