A truck is traveling due west at 31.1 km/h through a rain storm. The wind blows

Question

A truck is traveling due west at 31.1 km/h through a rain storm. The wind blows directly east so that the rain comes down making an angle of 10.0 degree with respect to the vertical. The rain traces on the side windows of the truck make an angle of 41.0 degree with the vertical (angled toward the rear of the truck). Determine the following. speed of the rain with respect to the Earth Draw a figure showing all velocities and all angles. Review the law of sines, m/s speed of the rain with respect to the truck

Explanation / Answer

w/r/t the earth, the rain has velocity V and therefore components
Vx = Vsin10º and
Vy = Vcos10º

The truck has velocity v.
tan41º = (Vx + v) / Vy = (Vsin10 + 31.1) / Vcos10

V = 45.57 km/h speed w/r/t earth = 12.65 m/s

w/r/t the truck,
V² = (45.57km/h*sin10 + 31.1km/h)² + (45.57km/h*cos10)² = 3536.03 (km/h)²
V = 59.46 km/h = 16.51 m/s

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