A car departs from a town and travels southeast at a constant speed of 40 mi/hr40~\text{mi/hr}. At 1:00\text{1:00} PM, the car passes its closest point to a tracking station, which is located 3 mi3~\text{mi} east of the town. What is the rate of change of the angle θ\theta between the tracking station and the car at 2:00\text{2:00} PM if the car continues on its path at the same speed? Use the Law of Sines and assume that the path of the car is straight. Round the answer to three decimal places.

dθdt≈0.053 radhr\frac{d\theta}{dt}\approx0.053~\frac{\mathrm{rad}}{\mathrm{hr}}

dθdt≈0.027 radhr\frac{d\theta}{dt}\approx0.027~\frac{\text{rad}}{\text{hr}}

dθdt≈0.071 radhr\frac{d\theta}{dt}\approx0.071~\frac{\mathrm{rad}}{\mathrm{hr}}

dθdt≈0.095 radhr\frac{d\theta}{dt}\approx0.095~\frac{\mathrm{rad}}{\mathrm{hr}}

A car departs from a town and travels southeast at a constant spe...

Introduction to Functions
(0)

Piecewise Functions
(0)

Properties of Functions
(0)

Common Functions
(0)

Transformations
(0)

Combining Functions
(0)

Exponent Rules
(0)

Exponential Functions
(0)

Logarithmic Functions
(0)

Properties of Logarithms
(0)

Exponential & Logarithmic Equations
(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

Tangent Lines and Derivatives
(0)

Derivatives as Functions
(0)

Basic Graphing of the Derivative
(0)

Differentiability
(0)

Basic Rules of Differentiation
(0)

Higher Order Derivatives
(0)

Product and Quotient Rules
(0)

The Chain Rule
(0)

Derivatives of Exponential & Logarithmic Functions
(0)

Implicit Differentiation
(0)

Logarithmic Differentiation
(0)

Related Rates
(0)

Differentials
(0)

Linearization
(0)

Intro to Extrema
(0)

The First Derivative Test
(0)

Concavity
(0)

The Second Derivative Test
(0)

Curve Sketching
(0)

Finding Global Extrema
(0)

Applied Optimization
(0)

Antiderivatives
(0)

Indefinite Integrals
(0)

Estimating Area with Finite Sums
(0)

Riemann Sums
(0)

Introduction to Definite Integrals
(0)

Fundamental Theorem of Calculus
(0)

Average Value of a Function
(0)

Substitution for Indefinite Integrals
(0)

Substitution for Definite Integrals
(0)

Area Between Curves
(0)

Introduction to Volume & Disk Method
(0)

Integrals of Exponential Functions
(0)

Integrals Involving Logarithmic Functions
(0)

Integration by Parts
(0)

Improper Integrals
(0)

Angles
(0)

Trigonometric Functions on Right Triangles
(0)

Solving Right Triangles
(0)

Trigonometric Functions on the Unit Circle
(0)

Graphs of Sine & Cosine
(0)

Graphs of Other Trigonometric Functions
(0)

Trigonometric Identities
(0)

Derivatives of Trig Functions
(0)

Integrals of Basic Trig Functions
(0)

Integrals of Other Trig Functions
(0)

Basics of Differential Equations
(0)

Slope Fields
(0)

Separable Differential Equations
(0)

Sequences
(0)

Review of Factorials
(0)

Series
(0)

Power Series & Taylor Series
(0)

Continuous Probability Models
(0)

Related Rates: Videos & Practice Problems