Answer:

a) To find the y-component of the velocity, we can use the fact that the maximum height occurs when the y-component of the velocity is zero. The y-component of the velocity at the maximum height is equal to the initial y-component of the velocity (Vy) minus the acceleration due to gravity (g) multiplied by the time taken to reach the maximum height (t). Since Vy = 0 at the maximum height, we can set up the equation:

0 = Vy - g * t_max

Solving for Vy, we get:

Vy = g * t_max

Given that the acceleration due to gravity is approximately 9.8 m/s², we can substitute this value and find the y-component of the velocity.

b) To determine the time the balloon is in the air, we need to find the total time it takes for the balloon to reach the maximum height and then come back down to the ground. Since the motion follows a parabolic path, the time taken to reach the maximum height is equal to the time taken to come back down. Thus, we can double the time taken to reach the maximum height to find the total time the balloon is in the air.

c) The x-component of the velocity remains constant throughout the motion. We can use the horizontal distance traveled (19.2 meters) and the total time in the air to find the x-component of the velocity using the equation:

x-component of velocity = horizontal distance / time

d) To find the speed and angle at which the balloon was launched, we can calculate the magnitude of the velocity and the angle above the horizontal. The magnitude of the velocity can be found using the equation:

velocity = sqrt((x-component of velocity)² + (y-component of velocity)²)

The angle above the horizontal can be found using the inverse tangent function:

angle = arctan((y-component of velocity) / (x-component of velocity))

By plugging in the values we calculated for the x-component and y-component of the velocity, we can find the speed and angle at which the balloon was launched.

Hope it Helps!! <33