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?
I don't see a way of determining how far it traveled when rising.
O ok. My teacher told us we had to separate it into 3 separate parts, but i'm not sure how to do that.
I agree with your teacher. But you need times for each part, you are given time for the last constant altitude part only.
OK, it just came to me.
Time rising= altitude/veloictyrising=202/1.1= XXXseconds.
during that time, it travels this horizontal distance:
distance=xxxxseconds*2.7m/s
Then add to that, the distance when at constant altitude
distance= 10.3*2.7m/s
To determine how far the sandbag will land from the launching station, we need to break down the motion of the hot air balloon and the sandbag into horizontal and vertical components.
First, let's calculate the time it takes for the sandbag to fall. We know that the sandbag is dropped when the balloon is at an altitude of 202 m. The time it takes for an object to fall from a certain height can be found using the formula for free-fall motion:
h = (1/2) * g * t^2
Where:
h = height (202 m in this case)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Rearranging the formula, we get:
t^2 = (2 * h) / g
t^2 = (2 * 202 m) / (9.8 m/s^2)
t^2 ≈ 41.2245 s^2
t ≈ √41.2245 s ≈ 6.42 s
Now that we have the time it takes for the sandbag to fall, we can calculate the horizontal distance it covers during this time. The horizontal distance is simply the product of the horizontal speed and the time:
distance = speed * time
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.