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 the edge of a 4.5m waterfall. The spy's speed is 16m/s and the official's speed is 24m/s. How far apart will the two vessels be when they land below the waterfall? The acceleration of gravity is 9.8m/s^2. Answer in units of m.
To calculate the distance between the two vessels when they land below the waterfall, we need to determine the time it takes for both boats to reach the waterfall and then use that time to calculate the distance traveled by each boat.
Let's start by finding the time it takes for each boat to reach the waterfall.
The spy's boat is moving at a speed of 16 m/s, so we can calculate the time it takes for the spy's boat to reach the waterfall using the equation:
time = distance / speed
Since the distance is not provided, we need to find it. However, we know that distance equals speed multiplied by time. We also know that the spy's boat has not been caught when it reaches the waterfall, so the time it takes for the spy's boat to reach the waterfall should be the same as the time it takes for the officials' boat.
Let's calculate the time it takes for both boats to reach the waterfall:
time = distance / speed
For the spy's boat:
time_spy = distance / 16 m/s
For the officials' boat:
time_officials = distance / 24 m/s
Since both times are equal, we can equate them:
distance / 16 m/s = distance / 24 m/s
To simplify the equation, we can multiply both sides by 16 m/s and 24 m/s:
24 m/s * distance = 16 m/s * distance
24 * distance = 16 * distance
This equation tells us that the distance traveled by each boat is the same. Therefore, the distance between the two vessels when they land below the waterfall is zero.
In other words, the boats will land at the same spot below the waterfall, and there will be no distance between them.