Question

# A tank is filled up to height 2H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground is ′Z′H where a small hole is punched to get the maximum range R then the value of ′Z′ is

Solution

## As we know, Range R=v×t  (where v is velocity and t is time) If we think in term of projectile motion then we can say x=12gt2   t=√2xg The velocity of flux can be writen asv=√2g(3H−x) where, (3H−x) is the height of the water lable above hole Now, R=√2g(3H−x)×√2xg R=√12Hx−4x2         Here, R=f(x) From above equation we can visualise that this is a quadratic equation and if we plot graph between R and x Due to symmetry, the maximum value of range will be at the centre and that will be at x=3H2  ⟹z=32=1.5  Physics

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