A stunt pilot is attempting to drop a water balloon from a moving airplane onto a target on the ground. The plane moves at a speed of 82.8 m/s and a 49° above the horizontal when the balloon is released. At the point of release, the plane is at an altitude of 700 m. At the point just before balloon strikes the ground, what angle does its velocity make with the horizontal? Give your answer as an angle measured below the horizontal.

To find the angle that the velocity of the water balloon makes with the horizontal just before it strikes the ground, we can break down the problem into two components: the horizontal component and the vertical component.

1. Find the vertical component:
Since the plane is flying at an angle of 49° above the horizontal, the vertical component of its velocity can be calculated using trigonometry.
Vertical component of velocity = Velocity × sin(angle)
Vertical component of velocity = 82.8 m/s × sin(49°)

2. Find the time it takes for the balloon to reach the ground:
We know that the initial altitude of the balloon is 700 m, and gravity is acting downward. We can use the equation of motion to find the time it takes for the balloon to reach the ground.
Height = (Vertical component of velocity) × time - (1/2) × acceleration due to gravity × time^2
0 = (Vertical component of velocity) × time - (1/2) × 9.8 m/s^2 × time^2

Rearranging the equation gives:
(1/2) × 9.8 m/s^2 × time^2 = (Vertical component of velocity) × time
(1/2) × 9.8 m/s^2 × time = (Vertical component of velocity)
time = (Vertical component of velocity) / [(1/2) × 9.8 m/s^2]

3. Find the horizontal component:
Since the plane is moving at a constant speed, the horizontal component of the velocity remains the same throughout the motion.
Horizontal component of velocity = Velocity × cos(angle)
Horizontal component of velocity = 82.8 m/s × cos(49°)

4. Find the total time of flight:
Since both the horizontal and vertical components of the motion take the same amount of time, the total time of flight can be calculated by dividing the initial altitude by the vertical component of velocity.
Total time of flight = 700 m / (Vertical component of velocity)

5. Find the horizontal displacement:
The horizontal displacement is given by the equation: Horizontal displacement = Horizontal component of velocity × Total time of flight

6. Find the vertical displacement:
Since the initial altitude is 700 m and the final altitude is 0 m, the vertical displacement is equal to the initial altitude.

7. Find the angle of the velocity with the horizontal just before it strikes the ground:
Using the horizontal and vertical displacements, we can find the angle using trigonometry.
angle = tan^(-1)(vertical displacement / horizontal displacement)

Plug in the values and solve the equations to find the angle.