Runner A is initially 5.3 km west of a flagpole and is running with a constant velocity of 8.4 km/h due east. Runner B is initially 4.5 km east of the flagpole and is running with a constant velocity of 7.1 km/h due west. How far are the runners from the flagpole when their paths cross? Answer in units of km
Va*t + Vb*t = Da + Db.
8.4t + 7.1t = 5.3 + 4.5
15.5t = 9.8
t = 0.63226 h = Time at which their paths cross.
d = 4.5 - 7.1*0.63226 = 4.5 - 4.489 =
0.01097 km = 11 m. East of flagpole.
To find out how far the runners are from the flagpole when their paths cross, we need to determine the time it takes for them to meet. Let's break down the problem:
Runner A is initially 5.3 km west of the flagpole and running east at a constant speed of 8.4 km/h. We can denote this as a displacement, dA = +5.3 km (east) and the velocity, vA = 8.4 km/h (east).
Similarly, Runner B is initially 4.5 km east of the flagpole and running west at a constant speed of 7.1 km/h. We can denote this as a displacement, dB = -4.5 km (west) and the velocity, vB = 7.1 km/h (west).
Since displacement is the change in position, we can set up an equation:
dA + dB = 0
Let's calculate the time it takes for Runner A and Runner B to meet:
To find the time, we can use the formula: time = distance / velocity.
For Runner A: timeA = dA / vA = (+5.3 km) / (8.4 km/h) = 0.631 hours.
For Runner B: timeB = dB / vB = (-4.5 km) / (7.1 km/h) = -0.634 hours.
Since both runners are moving towards each other, we can take the absolute values of their times:
timeA = |0.631| hours = 0.631 hours.
timeB = |(-0.634)| hours = 0.634 hours.
Now, let's calculate the distances covered by each runner during their meeting time:
For Runner A: distanceA = vA * timeA = (8.4 km/h) * (0.631 hours) = 5.3 km.
For Runner B: distanceB = vB * timeB = (7.1 km/h) * (0.634 hours) = 4.5 km.
Since both runners are moving towards each other, the total distance they are from the flagpole when they meet is the sum of their distances from the flagpole:
Total distance = distanceA + distanceB = 5.3 km + 4.5 km = 9.8 km.
Therefore, the runners are 9.8 km from the flagpole when their paths cross.