Raindrops leave a trace on the glass of the electric train at an angle of 30 ° to the vertical when it moves at a speed of V = 8 m / s.

| November 19, 2020 | education

Raindrops leave a trace on the glass of the electric train at an angle of 30 ° to the vertical when it moves at a speed of V = 8 m / s. At what speed must the train move so that this angle is 60 °?

V1 = 8 m / s.
α1 = 30 °.
α2 = 60 °.
V2 -?
The drop relative to the ground moves vertically downward, the drop velocity Vk is directed vertically downward. The train moves horizontally, the speed of the train V1 is directed horizontally.
The speed of the drop relative to the moving carriage will be the hypotenuse of a right-angled triangle with legs V1 and Vk.
tgα1 = V1 / Vк, where V1 is the speed of the electric train (horizontal), Vк is the speed of the drop (vertical).
Let us express the droplet velocity: Vк = V1 / tgα1.
tgα2 = V2 / Vк.
V2 = Vк * tgα2 = V1 * tgα2 / tgα1.
V2 = 8 m / s * tg60 ° / tg30 ° = 8 m / s * 2 = 16 m / s.
Answer: the speed of the train should be V2 = 16 m / s.



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