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 5.3
m waterfall. The spy’s speed is 15 m/s and
the officials’ speed is 24 m/s
what is your question
To determine what happens when the spy and the government officials reach the edge of the waterfall, we need to calculate the time it takes for each boat to reach the waterfall, as well as their positions when they reach the edge.
Let's start by calculating the time it takes for each boat to reach the waterfall.
Distance = Speed * Time
For the spy's boat:
Distance_spy = Speed_spy * Time_spy
For the government officials' boat:
Distance_officials = Speed_officials * Time_officials
Since the distance both boats need to cover is the same (the edge of the waterfall), we can set these two equations equal to each other:
Distance_spy = Distance_officials
Speed_spy * Time_spy = Speed_officials * Time_officials
Now, we can solve this equation for the time it takes for each boat to reach the waterfall.
Time_spy = (Speed_officials * Time_officials) / Speed_spy
We know the speed of the spy's boat is 15 m/s and the speed of the government officials' boat is 24 m/s. We need to solve for Time_officials.
Let's substitute the values in:
Time_spy = (24 m/s * Time_officials) / 15 m/s
Now we can solve for Time_officials:
Time_spy * 15 m/s = 24 m/s * Time_officials
15 Time_spy = 24 Time_officials
Time_officials = (15 Time_spy) / 24
Now, let's say the time it takes for the spy's boat to reach the waterfall is t seconds. We can substitute this value into the equation above:
Time_officials = (15 * t) / 24
Now we have the time it takes for the government officials' boat to reach the waterfall in terms of t.
Next, we can determine the positions of each boat when they reach the edge of the waterfall. We know the spy's boat travels at a constant speed of 15 m/s, so the position of the spy's boat will be:
Position_spy = Speed_spy * Time_spy
Position_spy = 15 m/s * t
Similarly, the position of the government officials' boat will be:
Position_officials = Speed_officials * Time_officials
Position_officials = 24 m/s * ((15 * t) / 24)
Simplifying:
Position_officials = 15 m/s * t
Now we have the positions of both boats when they reach the edge of the waterfall.
To determine what happens next, we need to compare the positions of the two boats. If the position of the government officials' boat is ahead of the spy's boat, it means they have caught up to the spy, and if the position of the spy's boat is ahead, it means the spy managed to escape.
If Position_officials < Position_spy, it means the government officials caught up to the spy.
If Position_officials >= Position_spy, it means the spy managed to escape.
By calculating the positions of the two boats and comparing them, we can determine the outcome of the chase when they reach the edge of the waterfall.