Superman to the Rescue!

Initial velocity of freely falling body (you) is $v_i = 200 m/s$ .

And the gravitational acceleration acting on you is $a = g = 10 m/s^2$ .

Initial and final velocities of Superman are same as no external force is acting on it i.e.

$v_i' = v_f' = v = 300 m/s \implies a = 0 m/s^2$

We can find the displacement of the falling body and Superman at any time using 2nd equation of motion i.e.,

$S = v_i \times t + 0.5a \times t^2$

For example displacements of falling body and Superman after $t = 1$ s would be 205 m and 300 m respectively.

But we have to find the time when the Superman meets the body in air. For this we can form an equation by equating the sum of displacements of both parties to the total distance between them i.e., 1200 m and then solving for time.

Displacement of falling body = $S_f = 200t + 0.5(10) \times t^2 = 200t + 5t^2$

Displacement of Superman = $S_p = 300t + 0.5(0) \times t^2 = 300t$

Now according to given condition,

$S_f + S_p = 1200$

$200t + 5t^2 + 300t =1200$

$5t^2 + 500t -1200 = 0$

Solving the quadratic equation for t gives two values: $2.34 , -102.34$ .

Since time cannot be negative, the only possible solution is $2.34$ which is the answer.