Math Problem Statement

A car travels due east with a speed of 38.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 64.0° with the vertical. Find the speed of the rain (in km/h) with respect to the car and the Earth. what is the speed of the earth in this question

Solution

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Math Problem Analysis

Mathematical Concepts

Relative Velocity
Trigonometry
Vector Addition

Formulas

tan(θ) = v_c / v_r
v_{rc} = sqrt(v_c^2 + v_r^2)

Theorems

Pythagorean Theorem
Trigonometric Functions

Suitable Grade Level

Grades 10-12