A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 9.15 is. The acceleration of gravity is 9.8 m/s2 . What is the height of the tower

The height of the tower is 20.764 m.

Explanation:

The angular frequency of the pendulum is:

The height of the lighthouse is:

The height of the tower is 20.764 m.

think its the third option

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft