A ball is attached to the moving end of the 5-meter arm of a pendulum. The pendulum swings through a 90 degree arc once. How far in meters, does the ball travel?
(pi/2) * R, where R = 5 meters
That is 1/4 of the circumference of a circle with radius R
1/4 divided by 3.14 x 10 is 7.9 meters
To find out how far the ball travels on the pendulum, we need to understand how the distance is related to the angle of swing.
In a pendulum, the distance traveled by the ball can be approximated using the arc length formula:
s = rθ
Where:
s is the distance traveled by the ball
r is the radius, which is the length of the pendulum's arm
θ is the angle of swing in radians
Given that the pendulum swings through a 90 degree arc, we need to convert this angle to radians since the formula requires angles in radians.
To convert degrees to radians, we use the following formula:
radians = degrees * (π/180)
Now let's calculate the angle in radians:
θ = 90 * (π/180) = π/2
Substituting the values into the arc length formula:
s = 5 * (π/2) = (5π)/2
Therefore, the ball travels approximately (5π)/2 meters.