A vertical cylindrical container of base area A and upper cross-section area $A_{1}$ making an angle 60° with the horizontal is placed in an open rainy field as shown near another cylindrical container having same base area A . Find the ratio of rates of collection of water in the two containers.

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TestHub · Accepted Answer

Collection rate = rain speed x horizontal projection of the opening (rain falls at 60° to the vertical as shown).

Tilted container: the slanted opening has area $A_{1} = \frac{A}{c o s 6 0 ^{\circ}}$ , and its horizontal projection is $A_{1} cos 6 0^{\circ} = A$ , so Rate $_{1} = v A$ .

Normal container: rain at 60° to the vertical gives Rate $_{2} = v A cos 6 0^{\circ} = \frac{v A}{2}$

$\frac{Rate _{1}}{Rate _{2}} = \frac{v A}{v A /2} = 2$ .

Answer: 2

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