Runner A is initially 9.0 mi west of a flagpole and is running with a constant velocity of 2.0 mi/h due east. Runner B is initially 5.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the flagpole when they meet?
v1•t+v2•t=s1+s2
t=(s1+s2)/(v1+v2) = 14/7 = 2 h.
v1•t=2•2=4 mi.
They met when they were 5 miles to the west from the flagpole
To find out how far the runners are from the flagpole when they meet, we can first calculate the time it takes for them to meet.
Runner A is initially 9.0 mi west of the flagpole and is moving with a velocity of 2.0 mi/h due east. Runner B is initially 5.0 mi east of the flagpole and is moving with a velocity of 5.0 mi/h due west.
Let's assume the time it takes for them to meet is represented by 't'.
Now, we can calculate the distance traveled by each runner using the equation:
distance = velocity * time
For Runner A:
distance_A = velocity_A * t
distance_A = 2.0 mi/h * t
For Runner B:
distance_B = velocity_B * t
distance_B = 5.0 mi/h * t
Since Runner A is moving east and Runner B is moving west, their distances will decrease as they move towards each other. The total distance between them at any time can be calculated by adding their distances relative to the flagpole:
total_distance = distance_A + distance_B
total_distance = (2.0 mi/h * t) + (5.0 mi/h * t)
total_distance = 7.0 mi/h * t
Now we set the total_distance equal to the initial distance between the runners:
total_distance = 9.0 mi + 5.0 mi
7.0 mi/h * t = 14.0 mi
Finally, we solve for the time 't':
t = 14.0 mi / 7.0 mi/h
t = 2.0 hours
Substituting this value back into the total distance equation:
total_distance = 7.0 mi/h * 2.0 h
total_distance = 14.0 mi
Therefore, when the runners meet, they are 14.0 miles from the flagpole.