A runner runs around a track consisting of two parallel lines 96m long connected at the ends by two semicircles with a radius of 49m. She completes one lap in 100 seconds. What is her average velocity
avg speed = distance/time, so that would be
(2*96 + 98π)/100 m/s
but since she ends up where she started, her average velocity is zero.
To find the average velocity, we need to divide the total displacement by the total time taken.
To calculate the total displacement, we need to find the total distance covered by the runner.
The runner runs around the two parallel lines and the two semicircles. First, let's find the distance covered around the parallel lines:
Distance covered around the parallel lines = length of one parallel line × 2
Distance covered around the parallel lines = 96 m × 2
Distance covered around the parallel lines = 192 m
Next, let's find the distance covered around the semicircles:
Distance covered around the semicircles = circumference of one semicircle × 2
To find the circumference of a semicircle, we use the formula: circumference = π × radius
Circumference of one semicircle = π × 49 m
Distance covered around the semicircles = π × 49 m × 2
Distance covered around the semicircles ≈ 307.94 m (approximate to two decimal places)
Now, let's find the total distance covered:
Total distance covered = distance covered around the parallel lines + distance covered around the semicircles
Total distance covered ≈ 192 m + 307.94 m
Total distance covered ≈ 499.94 m (approximate to two decimal places)
Now that we have the total distance covered, we can calculate the average velocity:
Average velocity = total distance covered / total time taken
Average velocity = 499.94 m / 100 s
Average velocity ≈ 4.999 m/s (approximate to three decimal places)
Therefore, the runner's average velocity is approximately 4.999 m/s.
To find the average velocity of the runner, we need to calculate the total distance covered and divide it by the total time taken.
First, let's calculate the distance traveled in each straight line segment of the track. Since there are two parallel lines of 96m each, the total distance covered in the straight line segments is 2 * 96 = 192m.
Next, let's calculate the distance covered in each semicircle. The formula to calculate the circumference of a circle is given by C = 2 * π * r, where r is the radius. Since we have semicircles, we need to divide the circumference by 2. Therefore, the distance covered in each semicircle is (π * r) = π * 49m = 49π m.
Since there are two semicircles in one lap, the total distance covered in the semicircles is 2 * 49π m.
Therefore, the total distance covered in one lap is 192m + 2 * 49π m.
Now, let's calculate the average velocity. The average velocity is defined as the total distance traveled divided by the total time taken. In this case, it is (192m + 2 * 49π m) / 100s.
To get the numerical value, we need to calculate the approximate value of π (pi). Let's use 3.14 for π.
Substituting the values, (192 + 2 * 49 * 3.14) / 100 = (192 + 307.12) / 100 = 499.12 / 100 ≈ 4.99 m/s.
Therefore, the average velocity of the runner is approximately 4.99 m/s.