Final answer:
The water balloon will be in the air for approximately 1.74 seconds and will land around 20.88 meters from the balcony. These calculations are based on the principles of projectile motion, considering the independence of horizontal and vertical components.
Step-by-step explanation:
To solve for the time the water balloon is in the air (a) and the distance it will land from the balcony (b), we apply the concepts of projectile motion to a water balloon launched horizontally. Because the horizontal and vertical motions are independent, we can address them separately.
The time the balloon is in the air depends solely on the vertical motion. Starting from rest, the balloon will accelerate downwards under gravity. We use the formula for distance under constant acceleration: d = ½gt², where d is the distance, g is the acceleration due to gravity (approximately 9.81 m/s²), and t is the time. Solving for t, we get a time of approximately 1.74 seconds.
The horizontal distance covered by the balloon can be calculated using the horizontal velocity and the time it was in the air. Because there is no horizontal acceleration, the horizontal distance x is simply the horizontal velocity v multiplied by the time t: x = vt. With a velocity of 12 m/s and a time of 1.74 seconds, the balloon will land approximately 20.88 meters from the balcony.