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:
[tex] X_{f} = X_{0} + v_{0}t + \frac{1}{2}at^{2} [/tex]
Where:
[tex]X_{f}[/tex] is the final position
[tex]X_{0}[/tex] 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:
[tex]X_{fA}+X_{fB}=5.8+4.9=10.7 km[/tex]
[tex]V_{A}t+V_{B}t=10.7[/tex]
[tex]8.6t+7.1t=10.7[/tex]
[tex]t = 0.68 h[/tex]
Now we can find the final distance of each runner.
[tex]X_{fA}=V_{A}*0.68[/tex]
[tex]X_{fA}=8.6*0.68 km[/tex]
[tex]X_{fA}=5.85 km[/tex]
[tex]X_{fB}=V_{B}*0.68[/tex]
[tex]X_{fB}=7.1*0.68[/tex]
[tex]X_{fB}=4.83 km[/tex]
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!
