Person A starts walking SW froma point at a speed of 13m/s. Ten seconds later person B starts walking from the same point and travels east at 10m/s. After person B have been walking 30 seconds, approximately how far apart are the two?
use the law of cosines
x^2 = (13*40)^2 + (10*30)^2 - 2(13*40)(10*30) cos 135°
To find approximately how far apart the two people are after person B has been walking for 30 seconds, we can first calculate the distances each person has traveled.
Person A starts walking southwest (SW) from a point at a speed of 13 m/s. Since person A starts before person B, we need to calculate the distance traveled by person A.
Distance traveled by person A = speed × time
Distance traveled by person A = 13 m/s × 10 s
Distance traveled by person A = 130 m
After 10 seconds, person B starts walking east at a speed of 10 m/s. To calculate the distance traveled by person B, we can use the same formula.
Distance traveled by person B = speed × time
Distance traveled by person B = 10 m/s × 30 s
Distance traveled by person B = 300 m
Since person A is traveling southwest and person B is traveling east, we can consider the distances they traveled as two sides of a right-angled triangle. The distance between the two people can be calculated using the Pythagorean theorem.
Distance between person A and person B = √(distance traveled by person A)^2 + (distance traveled by person B)^2
Distance between person A and person B = √(130^2 + 300^2)
Distance between person A and person B ≈ √(16900 + 90000)
Distance between person A and person B ≈ √106900
Distance between person A and person B ≈ 327.31 m
Therefore, approximately 327.31 meters apart.