Two runners start simultaneously at oppposite ends of a 200.0 m track and run toward each other. Runner A runs at a steady 8.0 m/s and runner B runs at a constant 7.0 m/s. When and where will these runners meet?
How do I start this problem
When two runners run toward each other from a distance D, it is like one person running the same distance, but with the sum of the two speeds.
Give it a try and see what you get.
I would start by recognizing that the tme of each runner is the same.
distance = rate*time.
Distance A runs is X. Distance B runs is 200-x.
Set the times equal and solve for x.
Part A: Total meters/rate1+rate2 = seconds
Part B: Faster rate * seconds = distance traveled
To solve this problem, you can start by finding out when the runners will meet and then determine their meeting point.
Step 1: Calculate the time it takes for the runners to meet.
To find when the runners will meet, you can use the formula: time = distance / speed. Runner A runs at 8.0 m/s, and Runner B runs at 7.0 m/s. Since they are running towards each other, you can consider their combined speed, which is 8.0 m/s + 7.0 m/s = 15.0 m/s.
Therefore, the time it takes for the runners to meet is: time = 200.0 m / 15.0 m/s.
Step 2: Calculate the distance Runner A has traveled when they meet.
Now that you have the time it takes for the runners to meet, you can calculate the distance Runner A has traveled during that time. Since Runner A runs at a constant speed of 8.0 m/s, their distance can be found using the formula: distance = speed x time.
Therefore, the distance Runner A has traveled is: distance = 8.0 m/s x (time calculated from Step 1).
Step 3: Determine the meeting point.
Since the runners start simultaneously at opposite ends of the track, you can calculate the meeting point by subtracting the distance Runner A has traveled from the total distance of the track, which is 200.0 m.
Therefore, the meeting point is: 200.0 m - (distance Runner A has traveled).
By following these steps, you can find both when the runners will meet and the location of their meeting point.