Solution:

To solve the problem, we can use the equations of motion under constant acceleration due to gravity. The key is to recognize that the time it takes to fall from a certain height is proportional to the square root of that height.

Let us assume that the body started falling from a height h above the upper point. Then, the time it took to fall the distance of 30 meters is given by:

t = sqrt(2*h/g) + sqrt(2*(h-30)/g)

where g is the acceleration due to gravity (approximately 9.8 m/s^2).

Simplifying the equation, we get:

t = sqrt(2/g)*(sqrt(h) + sqrt(h-30))

Now, we know that t = 1 second, so we can substitute that in the equation and solve for h:

1 = sqrt(2/g)*(sqrt(h) + sqrt(h-30))

1 = 0.446*(sqrt(h) + sqrt(h-30))

2.236 = sqrt(h) + sqrt(h-30)

Squaring both sides of the equation, we get:

5 = 2*sqrt(h)*sqrt(h-30)

Squaring again and simplifying, we get:

16h^2 - 480h + 900 = 0

Solving the quadratic equation, we get:

h = 32.1 m or h = 14.9 m

Since the body started falling from above the upper point, the answer is:

h = 32.1 m

Therefore, option (a) is the correct answer.

Summary:

- We can use the equations of motion under constant acceleration due to gravity to solve the problem.
- The time it takes to fall from a certain height is proportional to the square root of that height.
- We can set up an equation for the time it takes to fall 30 meters and solve for the initial height.
- The correct answer is h = 32.1 m.