You are keeping pace with another runner, at 4 minutes per mile, but are 16 m behind her when she is 130m from the finish line.At what pace will you be running at the finish?
*Express your answer using two significant figures.
Also, what is the constant acceleration do you need to catch her at the finish if she maintains a constant speed?
To solve this problem, we need to find the pace at which you will be running when you reach the finish line.
First, let's convert the distance into the same unit. The other runner is 130 meters away from the finish line, and you are 16 meters behind her. Therefore, you are 130 + 16 = 146 meters away from the finish line.
Next, let's determine the time it will take for you to cover this distance. We know that your pace is 4 minutes per mile. Since 1 mile is approximately 1609 meters, we can calculate your pace per meter by dividing 4 minutes by 1609 meters:
- 4 minutes/1609 meters = 0.002483 minutes/meter (rounded to 6 decimal places).
Now, we can find the time it will take for you to cover the remaining distance of 146 meters by multiplying the pace per meter by the distance:
- Time = Pace per meter × Distance
- Time = 0.002483 minutes/meter × 146 meters
Calculating this, we get:
- Time = 0.362, which is approximately 0.36 (rounded to two significant figures).
Thus, you will take approximately 0.36 minutes or 0.36 × 60 = 21.6 seconds to cover the remaining distance.
Therefore, your pace at the finish line will be approximately 0.36 minutes per mile, or 0.36 × 1609 = 580.24 meters per hour.
Finally, expressing the answer using two significant figures, your pace at the finish line will be approximately 580 meters per hour.