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 5.2 m waterfall. The spy’s speed is 15 m/s and the officials’ speed is 25 m/s.
How far apart will the two vessels be when they land below the waterfall? The accelera- tion of gravity is 9.81 m/s2 .
Answer in units of m
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To solve this problem, we need to calculate the time it takes for both boats to reach the bottom of the waterfall. Since both boats are traveling at a constant speed, we can use the formula:
time = distance / speed
Let's calculate the time for both boats separately:
For the spy's boat:
The speed of the spy's boat is given as 15 m/s. To calculate the time taken by the spy's boat to reach the bottom of the waterfall, we need to find the distance it travels before reaching the waterfall's edge. Since the officials' boat reaches the edge of the waterfall at the same time, we can assume that both boats travel the same distance until the waterfall's edge.
Given that the speed of the spy's boat is 15 m/s and time taken is t:
distance = speed * time
distance = 15 * t
For the officials' boat:
The speed of the officials' boat is given as 25 m/s. As mentioned earlier, both boats cover the same distance until reaching the waterfall's edge.
distance = speed * time
distance = 25 * t
Since both distances are equal, we can equate them:
15t = 25t
Solving for t:
10t = 0
t = 0
This implies that the time it takes for both boats to reach the waterfall's edge is zero. Consequently, the two boats will still be side by side when they land below the waterfall, and hence they will be 0 meters apart.