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 5.0
m waterfall. The spy’s speed is 15 m/s and
the officials’ speed is 24 m/s.How far apart will the two vessels be when
they land below the waterfall? The acceleration due to gravity is 9.81m/s^2. Assume friction and air resistance do not exist.

To determine how far apart the two vessels will be when they land below the waterfall, we need to figure out the time it takes for each boat to reach the bottom.

First, let's find the time it takes for the spy's boat to reach the bottom. Since we know the initial velocity (speed) of the spy's boat is 15 m/s and the distance (height of the waterfall) is 5.0 m, we can use the kinematic equation:

s = ut + (1/2)at^2

Where:
s = distance (5.0 m)
u = initial velocity (15 m/s)
a = acceleration due to gravity (-9.81 m/s^2, negative because it acts downwards)
t = time

Rearranging the equation, we get:

5.0 = 15t + (1/2)(-9.81)t^2

We can solve this quadratic equation to find the time it takes for the spy's boat to reach the bottom.

Now let's find the time it takes for the officials' boat to reach the bottom. Using the same equation, but with an initial velocity of 24 m/s, we'll solve for time again.

With the time it takes for each boat to reach the bottom, we can calculate the distance between them. Since they are traveling in the same direction and starting at the same point, the officials' boat will have traveled a distance (24 m/s) * (time) more than the spy's boat.

Plug in the calculated values to find the difference in distance between the two boats when they reach the bottom of the waterfall.