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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 ZH 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(3Hx) where, (3Hx) is the height of the water lable above hole
Now, R=2g(3Hx)×2xg
R=12Hx4x2         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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