On a hot summer evening, two Best Friends SG and Krishna decide to jump in a pool.

Both of them jumped into the pool at the same time and from the same spot. SG jumped with a horizontal velocity of $$50 \ ms^{-1}$$ and Krishna jumped with a horizontal velocity $$40 \ ms^{-1}$$ in the opposite direction.

The time at which their velocities are at $$90^{\circ}$$ with each other is of the form $$\sqrt{m} \ s$$. Find $$m$$.

(Take $$g=10 \ ms^{-2}$$. The image is not to scale.)

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