High School

A pendulum of length 1.10 m is released from rest at an angle of 52.0 degrees to the vertical. What will be the speed of the pendulum at the instant it reaches an angle of 41.6 degrees above the vertical?

A. 2.33 m/s
B. 4.61 m/s
C. 1.69 m/s
D. 2.88 m/s

Answer :

Final answer:

The speed of the pendulum at an angle of 41.6 degrees above the vertical is approximately 2.33 m/s.

Explanation:

To find the speed of the pendulum at a certain angle, we can use the conservation of mechanical energy. The formula to calculate the speed is given by v = sqrt(2gh(1 - cos(theta))), where v is the speed, g is the acceleration due to gravity, h is the height difference, and theta is the angle. In this case, the height difference is equal to 1.10m - 1.10m*cos(52.0) - 1.10m*cos(41.6). Substituting the values, we get v = sqrt(2 * 9.8 m/s^2 * (1.10m - 1.10m*cos(52.0) - 1.10m*cos(41.6)) * (1 - cos(41.6))). After calculating, the speed of the pendulum at that angle is approximately 2.33 m/s.

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