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While driving north at 25 m/s during a rainstorm you notice that the rain makes an angle of 38° with the vertical. while driving back home moments later at the same speed but in the opposite direction, you see that the rain is falling straight down. from these observations, determine the speed and angle of the raindrops relative to the ground?

User SilverArc
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1 Answer

3 votes

Answer:


v = 68.7 m/s

angle made with the vertical


\theta = 21.3 degree

Step-by-step explanation:

Velocity of rain with respect to the car with vertical direction makes 38 degree angle

so let say rain velocity is


v_r = v_x\hat i + v_y \hat j


v_(rc) = v_r - v_c


v_(rc) = (v_x + 25)\hat i + v_y

now we have


tan38 = (v_x + 25)/(v_y)

while return to home


v_(rc) = (v_x - 25)\hat i + v_y

now the angle with vertical is zero

so we have


v_x = 25

now we have


tan38 = (50)/(v_y)


v_y = 64 m/s

so we have


v_r = 25 \hat i + 64 \hat j

now magnitude of the speed is


v = √(25^2 + 64^2)


v = 68.7 m/s

angle made with the vertical


\theta = tan^(-1)(25)/(64)


\theta = 21.3 degree

User Igorpavlov
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