Question

Runner A is initially 5.8 km west of a flagpole and is running with a constant velocity of 8.6 km/h due east. Runner B is initially 4.9 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.

Answer 1

Answer:

Runner A will be 0.05 km from the flagpole, and runner B will be 0.07 km from the flagpole

Explanation:

We can find when their paths will cross as follows:

$X_{f} = X_{0} + v_{0}t + \frac{1}{2}at^{2}$

Where:

$X_{f}$ is the final position

$X_{0}$ is the initial position

v₀ is the initial speed

t is the time

a is the acceleration = 0 (since they are running with a constant velocity)

When their paths cross we have:

$X_{fA}+X_{fB}=5.8+4.9=10.7 km$

$V_{A}t+V_{B}t=10.7$

$8.6t+7.1t=10.7$

$t = 0.68 h$

Now we can find the final distance of each runner.

$X_{fA}=V_{A}*0.68$

$X_{fA}=8.6*0.68 km$

$X_{fA}=5.85 km$

$X_{fB}=V_{B}*0.68$

$X_{fB}=7.1*0.68$

$X_{fB}=4.83 km$

Therefore, runner A will be 0.05 km from the flagpole, and runner B will be 0.07 km from the flagpole.

I hope it helps you!