Calculating Velocity: Car and Earth in Motion – Help with Velocity Questions

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A car is traveling at 50 km/h due east while water falls vertically, creating a 60-degree angle with the vertical as seen from the car. To find the velocity of the water with respect to the car, a right triangle is used, leading to the calculation that the rain's velocity is approximately 28.87 km/h. The relationship between the car's velocity and the rain's velocity is established using trigonometry, specifically the tangent function. The hypotenuse of the triangle represents the apparent velocity of the rain as observed from the car. This approach clarifies the concept of "with respect to" in motion problems.
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velocity question help?

Homework Statement


A car is going at 50 km/h due east. Water is falling vertically with respect to the earth. Looking at the side windows the water creates a 60 degree angle with the vertical. What is the velocity of the water with respect to
a) car
b) earth.


Homework Equations



I don't know how to solve, so I don't know any relevant equations.

The Attempt at a Solution



Did not know how to approach. Could someone please clear this up for me. These type of "with respect to" questions are really confusing for me.
 
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Draw a 30-60-90 (right) triangle, with the 60 in the upper vertex (angle between hypotenuse and vertical leg).

The car travels a distance 50 km/h*T, and make that the length of the base.

In the same time T, the rain falls distance Vrain*T. Make that the other leg.

What is relationship between Vcar = 50 km/h and Vrain?
 
Astronuc said:
What is relationship between Vcar = 50 km/h and Vrain?

Tan 60 = 50 km/h / Vrain
Vrain=28.87 km/h

So that is the velocity of the rain with respect to the car. Would you just solve for the hypotenuse to get the velocity of the rain with respect to the earth.
 
just use trignometry...
 
The 28.9 km/h is the velocity (speed actually) of the rain (falling).

The hypotenuse would give the apparent velocity of the rain as observed from the car.
 
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