Ch 01: Units & VectorsWorksheetSee all chapters
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Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Solution: You leave the airport in College Station and fly 24.0 km in a direction 34.0° south of east. You then fly 46.0 km due north.How far must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?In what direction?

Solution: You leave the airport in College Station and fly 24.0 km in a direction 34.0° south of east. You then fly 46.0 km  m kmdue north.How far must you then fly to reach a private landing strip that is 32.0

Problem

You leave the airport in College Station and fly 24.0 km in a direction 34.0° south of east. You then fly 46.0 km due north.

How far must you then fly to reach a private landing strip that is 32.0 km due west of the College Station airport?

In what direction?

Solution

Steps for finding a missing vector:

  1. Write the vector equation for the problem (drawing a diagram usually helps a lot!)
  2. Decompose the given vectors and organize known information in a table.
  3. Write algebraic equations and solve.
  4. Find magnitude and angle of the resultant if required.

When writing a vector equation for one of these problems, it'll be in a form like 

A+B+...=R,

where the missing vector is one of the vectors on the left-hand side of the equation. Note that if the problem is about returning to the starting point, R=0.

For decomposing given vectors, we'll have to define a coordinate system if the problem hasn't, then use the equations

Ax=|A| cos θAy=|A| sin θ

If the final answer is supposed to be in magnitude-angle notation, we'll need to use these equations to get the magnitude and direction:

|A|=Ax2+Ay2

tan θ=AyAx

Step 1. This problem has the plane flying three separate legs (24.0 km at 34.0° south of east, 46.0 km north, and the unknown). We'll call them A, B, and C in order. The resultant R is 32.0 km west. So our vector equation is

A+B+C=R

Step 2. Define a coordinate system so that north is the +y-direction and east is the +x-direction. Then we can decompose vector A into x- and y-components. "South of east" in this coordinate system is counterclockwise from the +x-axis, so

Ax=|A| cos θ=(24.0 km) cos (-34.0°)=19.90 km  Ay=|A| sin θ=(24.0 km) sin (-34.0°)=-13.42 km

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