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 7.5 m waterfall. If the spy's speed is 19 m/s and the officials' speed is 24 m/s, how far apart will the two vessels be when they land below the waterfall?
time to fall 7.5m
7.5=1/2 g t^2 solve for t.
distance apart= relativevelocity*t
= 5m/s * t
3.87
To find out how far apart the two vessels will be when they land below the waterfall, we need to calculate the time it takes for each boat to reach the bottom of the waterfall.
Let's start by finding the time it takes for the spy's boat to reach the bottom of the waterfall:
Distance = Speed × Time
Since the distance the spy's boat travels is the same as the distance the officials' boat travels, we can set up the equation:
(19 m/s) × Time = (24 m/s) × Time
The time will cancel out from both sides of the equation, leaving us with:
19 m/s = 24 m/s
This means that the two boats will spend the same amount of time in the air.
Now we need to calculate the time it takes for a body to fall from a height of 7.5 m. To do that, we use the following formula:
Time = √(2 × Height ÷ Acceleration due to gravity)
The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Plugging in the values, we get:
Time = √(2 × 7.5 m ÷ 9.8 m/s^2)
Time = √(15 m ÷ 9.8 m/s^2)
Time = √1.53 s^2
Time ≈ 1.24 s
Since both boats spend the same amount of time in the air, they will land at the same time.
Now, let's calculate the distance each boat traveled during this time. We can use the following formula:
Distance = Speed × Time
For the spy's boat:
Distance = 19 m/s × 1.24 s
Distance ≈ 23.56 m
For the officials' boat:
Distance = 24 m/s × 1.24 s
Distance ≈ 29.76 m
So, when they land below the waterfall, the two vessels will be approximately 23.56 m apart from each other.