a rabbit starts running from point a in a straight line in the direction 52° from the north at 4.2 ft/sec. at the same time a fox starts running in a straight line from a position 23ft to the west of the rabbit at 7.9 ft/sec. the fox chooses its path so it will catch the rabbit at point c. in how many seconds will the fox catch the rabbit?
is that 52° east or west from north?
Now you need to know either point c or the direction chosen by the fox.
the 52° is east. the fox is running to catch the rabbit at point c which is east.
To determine the time it takes for the fox to catch the rabbit, we need to find the distance between the starting points of the rabbit and the fox and then divide it by the relative speed of the fox compared to the rabbit.
Let's break down the problem into steps:
Step 1: Find the distance between the starting points of the rabbit and the fox.
Given that the rabbit starts at point A and the fox starts 23 feet to the west of the rabbit, we can say that the distance between their starting points is 23 feet.
Step 2: Determine the relative speed of the fox compared to the rabbit.
The relative speed of the fox compared to the rabbit is the difference between their speeds. The rabbit runs at 4.2 ft/sec, while the fox runs at 7.9 ft/sec. Therefore, the relative speed is 7.9 ft/sec - 4.2 ft/sec = 3.7 ft/sec.
Step 3: Calculate the time it takes for the fox to catch the rabbit.
The time (in seconds) can be found by dividing the distance between the starting points by the relative speed of the fox:
Time = Distance / Relative Speed
Time = 23 ft / 3.7 ft/sec ≈ 6.22 seconds
Therefore, it will take approximately 6.22 seconds for the fox to catch the rabbit at point C.