Two runners approaching flagpole and displacement problem

[heatherly1004]

Hey guys, i am doing some physical science and i was stuck on some problems. I was wondering if anyone could help me out. thanks so much!


1. Runner A is initially 5.8 km west of a flagpole and is running with a constant velocity of 8.2 km/h due east. Runner B is initialy 4.8 km east of the flagpole and is running with a constant velocity of 7.8 km/h due west. How far are the runners from the flagpole when their paths cross?

2. While John is traveling along a straight interstate highway, he notices that the mile marker reads 252 km. John travels until he reaches the 149 km marker and then retraces his path to the 168 km marker. What is Johns resultant displacement from the 252 km marker?

 

[whozum]

1. I would set up some equations and solve them:

RA = -5.8km + 8.2km/h

RB = 4.8 - 7.8km/h

When they run into each other, they will both be at the same position, which means

RA = RB

-5.8km + 8.2km/h = 4.8 - 7.8km/h

If the units are confusing you, try changing it to:

8.2x-5.8 = -7.8x+4.8 and solve it for x.

This will tell you how long they were running when they intersect.

Take this and plug it into either one of the equations above, and find the distance the runner runs, then subtract that from his initial distance from the flagpole.

I'm really drowsy so if this is really confusing I am sorry.

2. I already answered in your other post

 

[thepatientmental]

1. To solve this problem, we can use the formula d = rt, where d is the distance, r is the rate (velocity), and t is the time. We know that Runner A is traveling at 8.2 km/h for a certain amount of time, and Runner B is traveling at 7.8 km/h for the same amount of time. Since their paths cross, we can set their distances equal to each other: 5.8 km + 8.2t = 4.8 km + 7.8t. Solving for t, we get t = 0.5 hours. Plugging this back into the formula, we can find the distance from the flagpole for each runner: Runner A travels 4.1 km and Runner B travels 3.9 km. Therefore, when their paths cross, they are both 3.9 km from the flagpole.

2. To find John's resultant displacement, we can use the formula d = d2 - d1, where d1 is the initial position and d2 is the final position. John's initial position is 252 km and his final position is 168 km. Therefore, his resultant displacement is 252 km - 168 km = 84 km. This means that John is 84 km from the 252 km marker when he reaches the 168 km marker.