Math Problem Statement
A train at a constant 42.0 km/h moves east for 28.0 min, then in a direction 54.0° east of due north for 24.0 min, and then west for 38.0 min. What are the (a) magnitude and (b) angle (relative to east) of its average velocity during this trip?
Solution
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Math Problem Analysis
Mathematical Concepts
Kinematics
Vectors
Trigonometry
Average Velocity
Formulas
Displacement = speed × time
Vector components: x = displacement × cos(θ), y = displacement × sin(θ)
Magnitude of displacement = sqrt(x^2 + y^2)
Average velocity = total displacement / total time
Angle = tan^(-1)(y / x)
Theorems
Pythagorean Theorem
Trigonometric Functions (Sine, Cosine, Tangent)
Suitable Grade Level
Grades 10-12
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