How much time can you save travelling diagonally instead of running 450meters south and then 650meters west. if your running speed is 5.0m/s.
pls help
To calculate the time saved by traveling diagonally instead of running 450 meters south and then 650 meters west, we need to compare the total time for both options.
First, let's calculate the time it takes to run south and then west:
Time to run south = Distance / Speed
Time to run south = 450 meters / 5.0 m/s
Time to run south = 90 seconds
Time to run west = Distance / Speed
Time to run west = 650 meters / 5.0 m/s
Time to run west = 130 seconds
Total time to run south and then west = Time to run south + Time to run west
Total time to run south and then west = 90 seconds + 130 seconds
Total time to run south and then west = 220 seconds
Now, let's calculate the time it takes to travel diagonally:
Distance in diagonal = √((450 meters)^2 + (650 meters)^2)
Distance in diagonal = √(202500 + 422500)
Distance in diagonal = √625000
Distance in diagonal = 790.6 meters (approximately)
Time to travel diagonally = Distance / Speed
Time to travel diagonally = 790.6 meters / 5.0 m/s
Time to travel diagonally = 158.12 seconds (approximately)
To calculate the time saved, we subtract the time to travel diagonally from the total time to run south and then west:
Time saved = Total time to run south and then west - Time to travel diagonally
Time saved = 220 seconds - 158.12 seconds
Time saved = 61.88 seconds (approximately)
Therefore, traveling diagonally instead of running 450 meters south and then 650 meters west can save approximately 61.88 seconds.
To determine how much time can be saved by travelling diagonally instead of running 450 meters south and then 650 meters west, we need to calculate the time taken for both scenarios and compare them.
First, let's calculate the time taken to run 450 meters south. We can use the formula: time = distance / speed.
Time taken to run 450 meters south = 450 meters / 5.0 m/s = 90 seconds.
Next, let's calculate the time taken to run 650 meters west.
Time taken to run 650 meters west = 650 meters / 5.0 m/s = 130 seconds.
Now, let's calculate the time taken to travel diagonally. This can be done using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the distance travelled diagonally forms the hypotenuse of a right triangle, and the distances travelled south and west form the other two sides.
Using the Pythagorean theorem, we can calculate the diagonal distance:
Diagonal distance = √(450^2 + 650^2) = √(202,500 + 422,500) = √625,000 = 790.6 meters (rounded to one decimal place).
Finally, let's calculate the time taken to travel diagonally:
Time taken to travel diagonally = diagonal distance / speed = 790.6 meters / 5.0 m/s = 158.1 seconds (rounded to one decimal place).
To calculate the time saved, we subtract the time taken to travel diagonally from the sum of the individual travel times:
Time saved = (time taken to run south + time taken to run west) - time taken to travel diagonally
= (90 seconds + 130 seconds) - 158.1 seconds
= 220 seconds - 158.1 seconds
= 61.9 seconds (rounded to one decimal place).
Therefore, by travelling diagonally instead of running 450 meters south and then 650 meters west, you can save approximately 61.9 seconds.
The diagonal distance is
sqrt[(450)^2 + (650)^2] = 790.6 m
The distance running south and then west is 450 + 650 = 1100 m.
The saving is distance is 1100 - 970.6 = 129.4 m
The saving in time is that distance divided by 5 m/s.