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 4.2 m waterfall. If the spy's speed is 20 m/s and the officials' speed is 24 m/s, how far apart will the two vessels be when they land below the waterfall?
m
To solve this problem, we need to determine the time it takes for the boats to reach the waterfall, and then calculate the distance traveled by each boat during that time.
First, let's find the time it takes for the boats to reach the waterfall. We can do this by dividing the distance to the waterfall by the speed of each boat.
For the spy's boat:
Distance = Speed × Time
4.2 m = 20 m/s × Time
Time = 4.2 m ÷ 20 m/s = 0.21 s
For the officials' boat:
Distance = Speed × Time
4.2 m = 24 m/s × Time
Time = 4.2 m ÷ 24 m/s = 0.175 s
Now that we know the time it takes for each boat to reach the waterfall, we can calculate the distance traveled by each boat during that time.
For the spy's boat:
Distance = Speed × Time
Distance = 20 m/s × 0.21 s = 4.2 m
For the officials' boat:
Distance = Speed × Time
Distance = 24 m/s × 0.175 s = 4.2 m
Since both boats traveled the same distance, they will land vertically below the waterfall, and their distance apart will be 0 meters.