An open rectangular tank `5m xx 4m xx 3m ` high containing water upto a height of 2m is accelerated horizontally along the longer side .
(a) Determine the maximum acceleration that can be given without spilling the water .
(b)Calculate the percentage of water spill over , if this acceleration is increased by 20 %

Explanation

(a)Volume of water remains constant .
`rArr ((3+y_(0))/2) 5 = 5xx2 ` or , `y_(0) = 1m `
` :. tan theta_(0) = (3-1)/5 = 0.4`
Since , `tan theta_(0) = (a_(0))/g ` , therefore `a_(0) = 0.4g = 4 m//s^(2)`
(b) When acceleration is increased by 20 %
` a = 1.2 a_(0) = 0.48 g `
` :. tan theta = a/g = 0.48`
Now , ` y = 3 - 5 tan theta = 3 - 5 (0.48) = 0.6 m `
Fraction of water split over = `(2 - ((3+0.6))/2)/2 = 0.1 `
Percentage of water split over = 10 %