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 7.8 m waterfall. If the spy's speed is 11 m/s and the officials' speed is 22 m/s, how far apart will the two vessels be when they land below the waterfall?

h = 0.5g*t^2 = 7.8 m.

4.9*t^2 = 7.8
t^2 = 1.59
Tf = 1.26 s. = Fall time for each boat.

d1 = V1*t = 22m/s * 1.26s. = 27.76 m.

d2 = V2*t = 11m/s * 1.26s. = 13.88 m.

d1-d2 = 27.76 - 13.88 = 13.72 m. Apart.

student

Well, it seems like the spy is in quite a sticky situation, doesn't it? But don't worry, we'll try to solve this while keeping the laughter flowing!

To figure out how far apart the two vessels will be when they land below the waterfall, we first need to find out how long it takes for both boats to reach the edge.

Let's start with the spy. With a speed of 11 m/s, we can calculate the time it takes for the spy's boat to reach the waterfall by dividing the distance traveled by the speed. Since we don't know the distance, we'll call it 'x'. So the time for the spy is x/11 seconds.

Next up, the officials. With a speed of 22 m/s, their time is also x/22 seconds.

Now, since both boats reach the edge of the waterfall at the same time, we can set up an equation:

x/11 = x/22

But don't worry, we won't drown ourselves in math! By cross-multiplying and simplifying the equation, we find that x = 22.

Now, we know the distance, which is 22 meters, that both boats will travel before the waterfall. And since they're traveling together, they'll be side by side. No separation yet! They might as well hold hands and scream together!

But, oh my, when they end up taking the plunge down the waterfall, things will get interesting. The fall itself is 7.8 meters. So once they fall off the edge, they'll be 7.8 meters apart.

So, to answer the question, when the two vessels land below the waterfall, they will be 7.8 meters apart. Now let's hope they can swim and smile while waving at each other!

To find the distance between the two vessels when they land below the waterfall, we can first calculate the time it takes for each vessel to reach the waterfall.

Let's start with the spy's boat. The spy's speed is 11 m/s, and the distance to the waterfall is not specified. Therefore, we need to find the time it takes for the spy's boat to reach the waterfall.

We can use the formula: distance = speed * time.

Let's represent the distance to the waterfall as "d". Therefore, the time taken by the spy's boat to reach the waterfall is: time = distance / speed.

Next, let's calculate the time it takes for the officials' boat to reach the waterfall. The officials' speed is 22 m/s, and we assume that they start from the same point as the spy. Therefore, the time taken by the officials' boat to reach the waterfall will also be: time = distance / speed.

Since both the spy and officials travel at different speeds, their times will not be the same. However, since they reach the waterfall simultaneously, we can equate their times and solve for "d".

(distance of the spy's boat) / (speed of the spy's boat) = (distance of the officials' boat) / (speed of the officials' boat)

d / 11 = d / 22

Solving for "d" gives us the distance to the waterfall.

d = 11 * 7.8 / (22 - 11)

Now that we have found the distance to the waterfall, we can calculate the distance between the two vessels when they land below the waterfall.

The official's boat is right next to the spy's boat when they reach the waterfall, so the initial distance between them is 0.

When they land below the waterfall, the spy's boat will have traveled the distance to the waterfall (d), and the officials' boat will have traveled 7.8 meters more than the spy's boat.

Thus, the distance between the two vessels when they land below the waterfall will be:

d + 7.8 meters

Substituting the value of "d" found earlier, we can calculate the final answer.