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Solution :
We know that :
Formula for Gravitational force is given by :
where, G is the gravitational constant
M is the mass of the bigger body
m is the mass of the smaller body
r is the distance between the two bodies.
And the formula for the centripetal force is given by :
where, m is the mass of the rotating body
v is the velocity
r is the radius of rotation of the body.
We know that mathematically, the gravitational force is equal to the centripetal force of the body.
Therefore,
Hence derived.
Time taken to reach water :
Now, initial vertical speed , u = 0 m/s.
By equation of motion :
Here, a = g = acceleration due to gravity = 9.8 m/s².
So,
Therefore, the height of the bridge is 3.46 m.
Hence, this is the required solution.