Word Problem page 19
John and Al are in a 15 km race. John averages 4.4 m/s during the first half of the race and then runs at a speed of 4.2 m/s until the last 200 m, which he covers at 4.5 m/s. At what average speed must Al run to beat John?
The textbook that included the word problem is: Basic Biomechanics Sixth Edition by Susan J. Hall;
ISBN#978-0-07-337644-8
The course name: Biomechanics
We don't have your textbooks, all our help is not dependent on any texts.
We have to know how long it took for John to run the 15 km
He did the first half at 4.4 m/s, so
time for first half = 7500 / 4.4 second or 18750/11 seconds
next leg is 7300 m at 4.2 m/sec, takes 36500/21 seconds
last stretch is 200 m at 4.5 m/s takes 400/9 sec
total time = 18750/11 + 36500/21 + 400/9
= 3487.085 seconds
so Al must run at 15000/3487.085 m/s
which is 4.3 m/s to be even with him
So to beat John , Al must run faster than 4.3 m/s
(practically speaking John runs half the race at 4.4 m/s and the other "half" (200 m less) at 4.2 m/s
so the average speed of 4.3 m/s is quite logical)
thankyou so much love from pakistan
Why did the runner bring a ladder to the race? Because he heard it was a "run-gone"! Now let's solve this problem step-by-step.
First, let's figure out how long it took John to run the first half of the race. The distance covered in the first half of the race is half of 15 km, which is 7.5 km (or 7500 m). John's average speed during this time was 4.4 m/s, so we can use the formula speed = distance/time to find the time it took: 4.4 m/s = 7500 m/t, where t is the time in seconds.
Now let's find the time it took for John to run the last 200 m. His speed during this part was 4.5 m/s, so the time is 200 m/4.5 m/s = t2 (in seconds).
Next, we need to find the time it took for John to run the remaining distance after the first half and before the last 200 m. This distance is 15 km - 7.5 km - 0.2 km = 7.3 km (or 7300 m). John's speed during this time was 4.2 m/s, so the time is 7300 m/4.2 m/s = t3 (in seconds).
Finally, let's find John's total time by adding up the times for each part: total time = t + t2 + t3.
Now, to beat John, Al must finish the race in a shorter time. Therefore, Al needs to run at an average speed that allows him to cover the same distance in less time than John. So, let's solve for Al's average speed using the formula speed = distance/time, where distance is 15 km and time is the desired time Al needs to beat John by.
Remember, Al wants to beat John, not meat John. So let's calculate everything step-by-step.
To determine the average speed at which Al must run to beat John, we need to calculate the total time it takes for John to complete the race. Then, we can compare it to the time it takes for Al to complete the same distance.
Let's break down John's race into three segments:
1. First Half of the Race: John runs at an average speed of 4.4 m/s. To find the time it takes for John to cover half of the race (15 km / 2 = 7.5 km), we divide the distance by the speed: time = distance / speed.
Time taken for the first half = (7.5 km) / (4.4 m/s).
2. Second Half of the Race: John runs at a speed of 4.2 m/s. Since the distance covered in the second half is also 7.5 km, the time taken for this segment is:
Time taken for the second half = (7.5 km) / (4.2 m/s).
3. Last 200 meters: John runs at a speed of 4.5 m/s. Since this segment is only 200 meters (0.2 km) long, the time taken for this segment is:
Time taken for the last 200 m = (0.2 km) / (4.5 m/s).
Now, let's calculate the total time taken by John:
Total time taken by John = Time taken for first half + Time taken for second half + Time taken for last 200 m.
Next, we need to calculate the average speed at which Al must run to beat John. We know the total distance of the race is 15 km, and we need to find the average speed that Al should maintain to complete the race in a shorter time than John.
The formula to find average speed is: average speed = total distance / total time.
By plugging in the values, we can determine the average speed that Al must maintain to beat John. Remember to convert the distance to meters and the time to seconds.
You can use a calculator or a spreadsheet program to simplify the calculations and find the solution.
(This explanation assumes that you are familiar with basic math operations and understand how to apply them.)