Solve the following problems.
1. The rider of a Ferris wheel moves at a rate of 0.18m/s2. If the rider is 5.0m from the center of the Ferris wheel, what is his/her velocity?
To find the rider's velocity, we need to use the equation:
velocity = (acceleration) * (distance).
Given that the rider's acceleration is 0.18 m/s^2 and the distance from the center of the Ferris wheel is 5.0 m, we can substitute these values into the equation:
velocity = (0.18 m/s^2) * (5.0 m).
Multiplying the values:
velocity = 0.9 m/s.
Therefore, the rider's velocity is 0.9 m/s.
To solve this problem, we need to use the concept of centripetal acceleration and tangential velocity.
The centripetal acceleration (a) of an object moving in a circular path can be calculated using the formula:
a = v^2 / r
Where:
- a is the centripetal acceleration
- v is the tangential velocity
- r is the radius of the circular path
In this problem, we are given the centripetal acceleration (0.18 m/s^2) and the radius (5.0 m) of the Ferris wheel. We need to find the tangential velocity (v).
Rearranging the formula, we have:
v = √(a * r)
Substituting the given values:
v = √(0.18 m/s^2 * 5.0 m)
Calculating the square root:
v ≈ √(0.9 m^2/s^2)
Simplifying:
v ≈ 0.95 m/s
Therefore, the rider's velocity on the Ferris wheel is approximately 0.95 m/s.
a = 1/2 r^2 θ
plug in your numbers
v = rω