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 5.1
m waterfall. The spy’s speed is 17 m/s and
the officials’ speed is 26 m/s.
How far apart will the two vessels be when
they land below the waterfall? The acceleration of gravity is 9.81 m/s
2
.
Answer in units of m

To find the distance between the two vessels when they land below the waterfall, we need to consider the time it takes for each boat to fall and the horizontal distance they cover during that time.

First, let's calculate the time it takes for each boat to fall. We can use the equation of motion for free fall:

h = (1/2)gt^2

Where h is the height of the waterfall (5.1 m), g is the acceleration due to gravity (9.81 m/s^2), and t is the time. Rearranging the equation, we get:

t = sqrt((2h) / g)

Substituting the given values:

t = sqrt((2 * 5.1) / 9.81)
t ≈ 1.014 seconds

Now, let's calculate the distance covered by each boat horizontally during this time. The speed of the spy's boat is 17 m/s, and the speed of the officials' boat is 26 m/s.

Distance covered by the spy's boat = speed * time
= 17 * 1.014 ≈ 17.238 m

Distance covered by the officials' boat = speed * time
= 26 * 1.014 ≈ 26.264 m

Therefore, when the two vessels land below the waterfall, they will be approximately 17.238 m apart.

Answer: The two vessels will be approximately 17.238 meters apart when they land below the waterfall.