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a stone projected up vertically with a velocity v,reaches points x,y,z in its path with velocities v/root5 , v/root10 , v/root15 respectively.find the ratio xy:yz?

v²-u² = 2aS.

Here initial velocity,   u=v m/s.

a=-9.8m/s².

Case 1:-

            Final velocity,             v= v/root5.

Therefore,                  S = (v²-u²)/2a

                                                = [(v/root5)²/ (2*-9.8)] (here it is pt x).

Case 2:-

            Final velocity,             v= v/root10

            Therefore,                  S = [(v/root10)²/ (2*-9.8)] (pt y).

Case 3:-

            Final velocity,             v= v/root15

            Therefore,                  S = [(v/root15)²/ (2*-9.8)] (pt z).

The ratio xy:yz    = [(v/root5)²/ (2*-9.8)] * [(v/root10)²/ (2*-9.8)] /

 [(v/root10)²/ (2*-9.8)] * [(v/root15)²/ (2*-9.8)]

= [(v/root5)² * (v/root10)²] / [(v/root10)² * (v/root15)²

= (v/root5)² * (root15/v)²

= 15/5

=3.