A spy in a speed boat is being chased down a river by government officials in a faster craft. Just as the officials' boat pulls up next to the spy's boat, both reach the edge of a 7.7 m waterfall. If the spy's speed is 19 m/s and the officials' speed is 29 m/s, how far apart will the two vessels be when they land below the waterfall?

The official's boat will be 12.6 meters in front of the spy's boat.

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11.11

To solve this problem, we need to find out how much time it will take for the two vessels to reach the waterfall and calculate the distance covered by each vessel during that time.

First, let's find the time it takes for each vessel to reach the waterfall. We'll use the formula:

time = distance / speed

For the spy's boat:
time = 7.7 m / 19 m/s ≈ 0.4053 seconds

For the officials' boat:
time = 7.7 m / 29 m/s ≈ 0.2655 seconds

Now, let's calculate the distance covered by each vessel during this time.

For the spy's boat:
distance = speed * time
distance = 19 m/s * 0.4053 s ≈ 7.717 m

For the officials' boat:
distance = speed * time
distance = 29 m/s * 0.2655 s ≈ 7.6915 m

Therefore, the two vessels will be approximately 7.717 meters and 7.6915 meters apart when they land below the waterfall.