A van drives at constant speed to the right. A partially filled rectangular fish

Question

A van drives at constant speed to the right. A partially filled rectangular fish aquarium of dimension L sits in the back of the van, with initial water height h0. Upon seeing a red stop light ahead, the driver applies the brakes, and the water shifts to the front as sketched. The acceleration vector a rightarrow is to the left and is constant (the car decelerates at a constant rate). During the deceleration, the height of the water at the front (right side) of the tank is 7h0/6, as indicated on the sketch. Ignoring any sloshing of the water, generate an expression for the magnitude of the deceleration a as a function of g, ho and L.

Explanation / Answer

we knw tht

tan = a/g

2ho/6L = a/g

a = 2hog/6L = hog/3L

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