A hot air balloon starts at its launching station and it goes at a horizontal speed of 2.7 m/s and a vertical wind of 1.1 m/s. Once it reaches an altitude of 202 m, it stays at that altitude for 10.3 s, which is when it drops a sandbag. How far will the sandbag land from the launching station?
To determine how far the sandbag will land from the launching station, we need to calculate the horizontal distance traveled by the hot air balloon during the time it takes for the sandbag to fall.
First, let's determine the time it takes for the sandbag to fall. We can use the formula for vertical displacement in free fall:
h = (1/2) * g * t^2
where:
h = vertical displacement (202 m in this case)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Simplifying the equation for time:
t = √(2h/g)
t = √(2 * 202 m / 9.8 m/s^2)
t ≈ √(41.2245 s^2)
t ≈ 6.42 s
Now that we know the time it takes for the sandbag to fall (6.42 s), we can calculate the horizontal distance traveled by the hot air balloon during this time.
Distance = speed * time
Since the hot air balloon is only moving horizontally with a speed of 2.7 m/s, the horizontal distance traveled will be:
Distance = 2.7 m/s * 6.42 s
Distance ≈ 17.33 m
Therefore, the sandbag will land approximately 17.33 meters away from the launching station.