an athlete completes one round of circular track of radius R in 40 second what will be his displacement at end of 2minutes 20 second
Nope, displscement is a vector.
displacement= ending position-starting position.
As I calculate, he is opposite his starting position, or 2R, in the direction opposite the starting point. In polar coordinates, the displacement is
2R@180
To find the displacement of the athlete, we need to determine how many rounds of the circular track he completes in 2 minutes and 20 seconds.
First, let's convert 2 minutes and 20 seconds to seconds:
2 minutes = 2 * 60 = 120 seconds
So, 2 minutes and 20 seconds = 120 + 20 = 140 seconds.
Now, let's find out how many rounds the athlete completes in 140 seconds.
Since he completes one round in 40 seconds, we can divide the total time by the time taken for one round:
Number of rounds = total time / time taken for one round
Number of rounds = 140 seconds / 40 seconds = 3.5 rounds
However, since we are dealing with displacement, and each round brings the athlete back to the starting point, we need to consider only the remaining distance after completing the whole number of rounds.
The displacement after 3 rounds will be zero because the athlete will end up at the starting point. The remaining 0.5 round (or half a round) will have a displacement.
To find the displacement for half a round, we use the formula:
Displacement = 2 * π * R
Where R is the radius of the circular track.
Therefore, the displacement for half a round is:
Displacement = 2 * π * R * 0.5 = π * R
So, the displacement of the athlete at the end of 2 minutes and 20 seconds will be π * R, considering half a round.
To find the displacement of the athlete, we need to first calculate the distance traveled in one round of the circular track, and then determine how many rounds he completes in 2 minutes and 20 seconds.
The distance traveled in one round of the circular track is equal to the circumference of the circle, which can be calculated using the formula:
Circumference = 2πR
Next, we need to determine how many rounds the athlete completes in 2 minutes and 20 seconds. We can convert 2 minutes and 20 seconds into seconds and then divide it by the time taken for one round (40 seconds) to get the number of rounds completed.
Once we know the number of rounds completed, we can calculate the displacement. The displacement for each round is equal to the circumference of the circle. Therefore, the total displacement is equal to the circumference multiplied by the number of rounds completed.
Let's calculate the displacement step by step:
Step 1: Calculate the circumference of the circular track.
Circumference = 2πR
Step 2: Convert 2 minutes and 20 seconds into seconds.
2 minutes = 2 * 60 = 120 seconds
20 seconds = 20 seconds
Total time = 120 + 20 = 140 seconds
Step 3: Determine the number of rounds completed.
Number of rounds = Total time / Time per round
Number of rounds = 140 seconds / 40 seconds (time per round)
Step 4: Calculate the displacement.
Displacement = Circumference * Number of rounds
By following these steps, you can find the displacement of the athlete at the end of 2 minutes and 20 seconds.
2minutes 20 secinds=3.5 rounds
circumfrence=2pieR
displacement=7x22/7xr
=22r
So the displacement will be 22r