A carnival swing is fixed on the end of an 7.7-m-long beam. If the swing and beam sweep through an angle of 100°, what is the distance through which the riders move?
Well, with that much swing, I hope those riders don't get motion "squeasiness!"
But to answer your question, we can calculate the distance using some trigonometry. The distance through which the riders move will depend on the length of the arc formed by the angle and the radius of the swing.
In this case, the radius is 7.7 m, and the angle is 100°. To calculate the arc length (or distance), we use the formula:
Arc Length (s) = (angle in radians) x (radius)
However, we need to convert the angle from degrees to radians first. Given that 180° is equivalent to π radians, we can find the arc length:
Arc Length (s) = (100° x π/180) x 7.7 m
After simplifying, the arc length is approximately 13.468 meters.
So, the riders move about 13.468 meters during their adventurous swing! Just try not to swing too high, or they might say "Are we in orbit yet?!"
To find the distance through which the riders move, we need to find the length of the arc swept by the swing and beam.
The formula for the length of an arc is given by:
Arc Length = (angle / 360) × (2 × π × radius)
In this case, the angle is given as 100° and the radius is the length of the beam, which is 7.7 meters.
Plugging in the values, we get:
Arc Length = (100 / 360) × (2 × π × 7.7)
= (10 / 36) × (2 × 3.14 × 7.7)
= (10 / 36) × (2 × 3.14 × 7.7)
≈ 1.74 × 7.7
≈ 13.38 meters
Therefore, the distance through which the riders move is approximately 13.38 meters.
To find the distance through which the riders move, we need to calculate the arc length of the swing's motion.
The arc length can be determined using the formula:
Arc length = (θ/360) x 2πr
where θ is the angle in degrees and r is the radius.
In this case, the angle θ is given as 100° and the radius is the length of the beam, which is 7.7 meters.
Using the given values, we can calculate the arc length as follows:
Arc length = (100/360) x 2π x 7.7
= (5/18) x 2π x 7.7
≈ 5.39 meters
Therefore, the riders move approximately 5.39 meters.