If a discus thrower rotates through the last 45 degrees of a turn in .11 seconds and the distance from the axis of the rotation to the center of the discus is 1.22 m, what is the average linear velocity of the discus?
what does PI stand for?
To find the average linear velocity of the discus, we can use the formula:
Average linear velocity = (angle rotated / time taken) * distance from axis to center
Given that the discus thrower rotates through the last 45 degrees of a turn in 0.11 seconds and the distance from the axis of rotation to the center of the discus is 1.22 m, we can substitute the values into the formula:
Average linear velocity = (45 degrees / 0.11 s) * 1.22 m
First, we need to convert the angle from degrees to radians because we are using the metric system:
45 degrees = (45 degrees * π / 180 degrees) radians
= (π / 4) radians
Now we can calculate the average linear velocity:
Average linear velocity = ((π / 4) radians / 0.11 s) * 1.22 m
≈ 3.513 m/s
Therefore, the average linear velocity of the discus is approximately 3.513 m/s.
To find the average linear velocity of the discus, we need to divide the distance traveled by the time taken.
First, let's find the distance traveled by the discus during the last 45 degrees of the turn. To calculate this, we need to find the circumference of the circle described by the discus at a distance of 1.22 m from the axis of rotation.
The formula for the circumference of a circle is given by:
C = 2πr
Where C is the circumference and r is the radius.
Since the radius is given as 1.22 m, we can substitute the value into the formula:
C = 2π(1.22)
Now, let's calculate the circumference:
C = 2π(1.22)
C ≈ 7.65 m
So, the distance traveled by the discus during the last 45 degrees of the turn is approximately 7.65 m.
Next, we divide this distance by the time taken to find the average linear velocity:
Average linear velocity = Distance traveled / Time taken
Average linear velocity = 7.65 m / 0.11 s
Now, let's calculate the average linear velocity:
Average linear velocity ≈ 69.5 m/s
Therefore, the average linear velocity of the discus is approximately 69.5 m/s.