Part C Two cyclists start on a race between points A and D on two different routes cyclist takes the route passing through the equidistant points A Deach separated by a distance of 200 meters Y takes the direct route which has a total length of 46.41 meters Both cyclists reach the end point in 30 seconds Calculate the displacement and average velocities of cyclists and Y.
To calculate the displacement and average velocities of both cyclists, we first need to understand the concepts of displacement and velocity.
Displacement is the change in position of an object. It is generally represented as a vector quantity, meaning it has both magnitude (distance) and direction. In this case, we need to find the displacement between points A and D for both cyclists.
Velocity, on the other hand, is the rate at which an object changes its position. It is also a vector quantity, represented as the displacement divided by the time taken. The average velocity is the total displacement divided by the total time.
Let's calculate the values step by step:
Step 1: Calculate the displacement for each cyclist.
For cyclist X:
Since cyclist X takes the route passing through the equidistant points A and D, we can assume that cyclist X travels along a straight line between A and D. Thus, the displacement for cyclist X is the straight-line distance between points A and D, which is 200 meters.
For cyclist Y:
Cyclist Y takes the direct route, so the displacement for cyclist Y is the straight-line distance between points A and D, which is also 200 meters.
Step 2: Calculate the average velocities for each cyclist.
The average velocity is given by total displacement divided by total time.
For cyclist X:
Displacement = 200 meters
Total time taken = 30 seconds
Average velocity = Displacement / Total time taken = 200 meters / 30 seconds
For cyclist Y:
Displacement = 200 meters
Total time taken = 30 seconds
Average velocity = Displacement / Total time taken = 200 meters / 30 seconds
To calculate the numerical values, we need to perform the division:
Average velocity for cyclist X = 200 meters / 30 seconds
Average velocity for cyclist Y = 200 meters / 30 seconds
By performing the division, we find that the average velocities for both cyclists are the same, as their displacements and times taken are equal.
Therefore, the displacement for both cyclists is 200 meters, and their average velocities are 6.67 meters/second.