Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 4.5 km/h due east. Runner B is initially 8.0 km east of the flagpole and is running with a constant velocity of 6.5 km/h due west
-How much time does it take for the runners to cross?
-How far is runner A from the start of the race when the runners cross?
- How far are the runners from the flagpole when their paths cross?
___ km east of the flagpole or
___ km east of the flagpole
To find the time it takes for the runners to cross, we need to calculate their relative velocity and divide the distance between them by that velocity.
Runner A is running east at a velocity of 4.5 km/h, and runner B is running west at a velocity of 6.5 km/h. Since they are moving in opposite directions, their relative velocity is the sum of their individual velocities, which is 4.5 km/h + 6.5 km/h = 11 km/h.
The distance between runner A and runner B is the sum of their displacement from the flagpole, which is 6.0 km (west) + 8.0 km (east) = 14.0 km.
To find the time it takes for the runners to cross, we divide the distance by the relative velocity: time = distance / velocity = 14.0 km / 11 km/h = 1.27 hours.
Therefore, it takes 1.27 hours for the runners to cross.
To find how far runner A is from the start of the race when the runners cross, we need to find out how much distance runner A covers during this time.
Runner A's velocity is 4.5 km/h, and the time it takes for the runners to cross is 1.27 hours. Therefore, the distance runner A covers is distance = velocity * time = 4.5 km/h * 1.27 hours = 5.715 km.
Therefore, runner A is 5.715 km from the start of the race when the runners cross.
To find how far the runners are from the flagpole when their paths cross, we calculate the total distance travelled by each runner during the time it takes for them to cross.
Runner A's velocity is 4.5 km/h, and the time it takes for the runners to cross is 1.27 hours.
Therefore, the distance covered by runner A is distance = velocity * time = 4.5 km/h * 1.27 hours = 5.715 km.
Runner B's velocity is 6.5 km/h, and the time it takes for the runners to cross is 1.27 hours.
Therefore, the distance covered by runner B is distance = velocity * time = 6.5 km/h * 1.27 hours = 8.255 km.
To find how far the runners are from the flagpole when their paths cross, we calculate the difference in distance between runner A and runner B:
distance = |5.715 km - 8.255 km| = 2.54 km.
Therefore, the runners are 2.54 km east of the flagpole when their paths cross.