Answer:
[tex]a_y = 4.9\ m/s^2[/tex]
Explanation:
Given,
Width of rectangular tank, b = 1 m
Length of the tank, l = 2 m
height of the tank, d = 1.5 m
Depth of gasoline on the tank, h = 1 m
[tex]\dfrac{dz}{dy}=-\dfrac{1.5-1}{1}[/tex]
[tex]\dfrac{dz}{dy}=-0.5[/tex]
The differential form with the acceleration
[tex]\dfrac{dz}{dy}=\dfrac{-a_y}{a_z + g}[/tex]
[tex]-0.5=-\dfrac{a_y}{a_z + g}[/tex]
acceleration in z-direction = 0 m/s²
g = 9.8 m/s²
a_y is the horizontal acceleration of the gasoline.
[tex]0.5=\dfrac{a_y}{0 + 9.8}[/tex]
[tex] a_y = 9.8\times 0.5[/tex]
[tex]a_y = 4.9\ m/s^2[/tex]
Hence, Horizontal acceleration of the gasoline before gasoline would spill is equal to 4.9 m/s²
