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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 boats reach and leave the edge of an 8.0 m waterfall, horizontally. If the spy’s speed is 18.9 m/s and the officials’ speed is 21.2 m/s, how far apart in meters will the two vessels be when they land below the waterfall?

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Final answer:

The question is a physics problem dealing with projectile motion, where two boats travel horizontally while falling off a waterfall. The problem can be solved by calculating the free fall time and then multiplying it by each boat's horizontal speed to determine their respective distances traveled.

Step-by-step explanation:

The problem described is a classic case of projectile motion in physics, specifically addressing horizontal displacement while in free fall. Because both boats are at the same altitude when they leave the waterfall, they'll take the same amount of time to hit the water below. This time only depends on the vertical height from which they fall and gravity, and is independent of their horizontal velocities.

To find out how far apart the boats will be when they land, we use their respective horizontal speeds. We calculate the time it takes for the boats to fall using the formula for the time of free fall: t = sqrt(2h/g), where h is the height of the waterfall and g is the acceleration due to gravity (approx. 9.81 m/s2). Once we have the time, we multiply each boat's horizontal speed by this time to find the horizontal distance each boat will cover. Finally, we subtract the distances to find the separation.

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