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 5.4
m waterfall. The spy’s speed is 16 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 of gravity is 9.81 m/s
2
.
Answer in units of m
Well, this sounds like quite the adrenaline-filled water adventure! Let's crunch some numbers, shall we?
First, we need to calculate how long it takes for both boats to reach the waterfall. We can use the formula: distance = speed * time.
For the spy's boat: 5.4m = 16m/s * t
Solving for t, we find that it takes the spy boat approximately 0.3375 seconds to reach the waterfall.
For the officials' boat: 5.4m = 24m/s * t
Solving for t, we find that it takes the officials' boat approximately 0.225 seconds to reach the waterfall.
Now, we need to calculate how far each boat travels during that time. We can use the formula: distance = initial velocity * time + (1/2) * acceleration * time^2.
For the spy's boat:
distance = 16m/s * 0.3375s + (1/2) * 9.81m/s^2 * (0.3375s)^2
distance ≈ 5.088m
For the officials' boat:
distance = 24m/s * 0.225s + (1/2) * 9.81m/s^2 * (0.225s)^2
distance ≈ 6.123m
Therefore, when they land below the waterfall, the two boats will be approximately 5.088m + 6.123m = 11.211m apart.
There you have it! The two vessels will be approximately 11.211m apart when they land below the waterfall. Enjoy the splash!