Question

Runner A is initially 6.0 km west of a flagpole and is running with a constant velocity of 9.0 km/h due east. Runner B is initially 5.0 km east of the flagpole and is running with a constant velocity of 8.0 km/h due west. What will be the distance of the two runners from the flagpole when their paths cross? (It is not necessary to convert your answer from kilometers to meters for this problem. You may leave it in kilometers.)

Answer 1

Answer:

0.176m from the flagpole, westward.

Explanation:

Let the Eastward be the positive direction. So initially runner A is at position -6km, running with velocity of 9km/h while runner B is at position 5km running at a velocity of -8km/h. We can conduct the following equation for their distances over the same time t

$s_A = -6 + 9t$

$s_B = 5 - 8t$

When A an B meets, they are at the same position and at the same time. So

$s_A = s_B$

$-6 +9t = 5 - 8t$

$17t = 5 + 6 = 11$

$t = 11/17 = 0.647 s$

$s_A = -6 + 9*0.647 = -0.176 m$

So where they meet is 0.176m from the flagpole, westward.