A tank is filled up to a height 2H WITH A LIQUID and is placed on a platform of height H from the ground .the distance x from the ground where a small hole is punched to get maximum range R is?
Ans) let the distance be x.then range(R)=2 . [(3H-x).x]^1/2 ......................... [ since t=(2x/g)^1/2 and v={2g(3H-x)}^1/2 ] R^2 = 4.(3Hx-x^2) for R to be max...R^2 should be max.hence differentiating and putting d(R^2)/dx=0.we get 3H-2x=0x=3H/2.