What Happens When Krishna and SG Jump Together?

Classical Mechanics Level 3

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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