A vertical wind screen of a car is made up of two parts, as shown in figure-1.162, where the upper one A is 25 cm vertically long and covers the 5 cm of the lower piece B . The upper one is hinged at

Question

A vertical wind screen of a car is made up of two parts, as shown in figure-1.162, where the upper one $A$ is 25 cm vertically long and covers the 5 cm of the lower piece $B$ . The upper one is hinged at the top so that it can be opened outward, inclining to the vertical. The car is running on the horizontal road at 60 km/hr in the rain which is falling vertically at 20 km/hr. Find the maximum angle, through which the upper part $A$ can be opened outward,

such that the rain drops do not enter the car.

TestHub · Accepted Answer

In the car frame the rain falls at tan − 1 20 60 ​ = 71. 6 ∘ to the vertical, sloping down toward the car. With the hinge H at the top, the lower edge of A is E = ( 25 sin θ , − 25 cos θ ) and the top edge of B is T = ( 0 , − 20 ) cm (the closed overlap is 5 cm). Rain grazing E travels along slope 3 : 1 and crosses the plane of B at y = − 25 cos θ − 3 25 ​ sin θ ; it is blocked by B only if this is at or below T : 25 cos θ + 3 25 ​ sin θ ≥ 20 , i.e. 3 cos θ + sin θ ≥ 2.4 . Equality: 10 ​ cos ( θ − 18.4 3 ∘ ) = 2.4 , θ − 18.4 3 ∘ = 40. 6 ∘ , θ max ​ = 5 9 ∘ . Matches the printed answer.

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