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Physics help!?
A truck is traveling due west at 30.4 km/h through a rain storm. The wind blows directly east so that the rain comes down making an angle of 10.0° with respect to the vertical. The rain traces on the side windows of the truck make an angle of 54.0° with the vertical (angled toward the rear of the truck). Determine the following.
a) speed of the rain with respect to the Earth
b) speed of the rain with respect to the truck
1 Answer
- NCSLv 76 years agoFavorite Answer
Vrain w/r/t earth = Vrain w/r/t truck + Vtruck w/r/t earth
Vr/e*sin10 i + Vr/e*cos10 j = Vr/t*sin54 i + Vr/t*cos54 j - 30.4km/h i + 0 j
Now let's look just at the east-west ("x," or "i") components:
Vr/e*sin10 = Vr/t*sin54 - 30.4km/h
and now just the north-south ("y," or "j") components:
Vr/e*cos10 = Vr/t*cos54
Then Vr/e = Vr/t * 0.6 → plug this into the horizontal equation
Vr/t * 0.6 * sin10 = Vr/t * sin54 - 30.4km/h
Vr/t = 30.4km/h / 0.705 = 43 km/h ◄ (b) speed of rain w/r/t truck
Vr/e = Vr/t * 0.6 = 25.9 km/h ◄ (a) speed of rain w/r/t Earth
Hope this helps!
