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 4.6
m waterfall. The spy’s speed is 16 m/s and
the officials’ speed is 27 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.
how long does it take to fall 4.6m?
4.9t^2 = 4.6
t = 0.9689 s
(what a useless exercise. why not just make it 4.9m, or something more interesting?)
The difference in their speeds is 11 m/s
so they will be 11*0.9689 = 10.66 meters apart when they land.
Thank you so much!
To find the distance between the two vessels when they land below the waterfall, we need to calculate the time it takes for each boat to reach the edge of the waterfall and then multiply that time by the speed of the other boat.
First, let's find the time it takes for the spy's boat to reach the edge of the waterfall. We can use the equation:
distance = initial velocity × time + 0.5 × acceleration × time^2
In this case, the initial velocity of the spy's boat is 16 m/s, the acceleration is -9.81 m/s^2 (negative because it is upwards against gravity), and the distance is 4.6 m.
Plugging in the values, we have:
4.6 = 16t - 0.5 × 9.81 × t^2
Now, let's find the time it takes for the officials' boat to reach the edge of the waterfall. Using the same equation, but with an initial velocity of 27 m/s, an acceleration of -9.81 m/s^2, and a distance of 4.6 m, we have:
4.6 = 27t - 0.5 × 9.81 × t^2
We have a quadratic equation, so we can solve it by setting the equations equal to each other:
16t - 0.5 × 9.81 × t^2 = 27t - 0.5 × 9.81 × t^2
Simplifying the equation, we get:
10t = 27t
Dividing both sides by 10, we have:
t = 27/10 = 2.7 seconds
Now that we have the time it takes for the spy's boat to reach the edge of the waterfall, we can calculate the distance between the two vessels when they land below the waterfall. We use the equation:
distance = speed × time
For the spy's boat, the distance is:
distance = 27 m/s × 2.7 s = 72.9 m
So the two vessels will be approximately 72.9 meters apart when they land below the waterfall.