The rider to 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?
The given is 0.18m/s2 and 5.0m
a = v^2/r, so
.18 = v^2/5
Now just find v.
To find the rider's velocity, we need to use the formula for acceleration:
acceleration = change in velocity / change in time.
In this case, the acceleration is given as 0.18 m/s^2. Since the velocity is changing over time, we need to find the change in velocity. However, the problem does not provide the change in time.
To find the velocity, we can use the equation for centripetal acceleration:
acceleration = (velocity^2) / radius.
Rearranging the equation, we get:
velocity = sqrt(acceleration * radius).
Plugging in the values we know, the radius is given as 5.0 m, and the acceleration is given as 0.18 m/s^2:
velocity = sqrt(0.18 * 5.0).
Evaluating this expression:
velocity ≈ sqrt(0.9).
Finally, calculating the square root of 0.9:
velocity ≈ 0.9487m/s.
Therefore, the rider's velocity is approximately 0.9487 m/s.