Review Conceptual Example 2 in preparation for this problem. In Figure 5.4, an object, after being released from its circular path, travels the distance OA in the same time it would have moved from O to P on the circle. The speed of the object on and off the circle remains constant at the same value. Suppose that the radius of the circle in Figure 5.4 is 3.2 m and the angle is è is 24°. What is the distance OA?
The distance on the circle is (24/360)2PI*r
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To find the distance OA, we can use the information given in the problem: the radius of the circle (r = 3.2 m) and the angle (θ = 24°).
First, we need to calculate the length of the arc that corresponds to the angle θ on the circle. The formula to calculate the length of an arc is given by:
Arc length = (θ/360) × (2πr)
Substituting the given values into the formula:
Arc length = (24/360) × (2π × 3.2)
Simplifying the expression:
Arc length = (0.067) × (6.28)
Arc length = 0.421 m
Therefore, the length of the arc is 0.421 m.
Next, we need to find the distance OA, which is the same as the length of the arc in this scenario.
Therefore, the distance OA is 0.421 m.