Exam 1: Introduction and Mathematical Concepts

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Use the component method of vector addition to find the resultant of the following three vectors: Use the component method of vector addition to find the resultant of the following three vectors:   = 56 km, east   = 11 km, 22° south of east   = 88 km, 44° west of south = 56 km, east Use the component method of vector addition to find the resultant of the following three vectors:   = 56 km, east   = 11 km, 22° south of east   = 88 km, 44° west of south = 11 km, 22° south of east Use the component method of vector addition to find the resultant of the following three vectors:   = 56 km, east   = 11 km, 22° south of east   = 88 km, 44° west of south = 88 km, 44° west of south

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A certain mountain road is inclined 3.1° with respect to the horizon. What is the change in altitude of the car as a result of its traveling 2.90 km along the road?

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The Boston Marathon is the oldest annual foot race, in which those that finish complete a distance of 26 miles, 385 yards. Express this distance in kilometers.

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A runaway dog walks 0.64 km due north. He then runs due west to a hot dog stand. If the magnitude of the dog's total displacement vector is 0.91 km, what is the magnitude of the dog's displacement vector in the due west direction?

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Two vectors Two vectors   and   , are added together to form the vector   =   +   . The relationship between the magnitudes of these vectors is given by: C<sub>x </sub>= A cos 30° + B and C<sub>y </sub>= -A sin 30°. Which statement best describes the orientation of these vectors? and Two vectors   and   , are added together to form the vector   =   +   . The relationship between the magnitudes of these vectors is given by: C<sub>x </sub>= A cos 30° + B and C<sub>y </sub>= -A sin 30°. Which statement best describes the orientation of these vectors? , are added together to form the vector Two vectors   and   , are added together to form the vector   =   +   . The relationship between the magnitudes of these vectors is given by: C<sub>x </sub>= A cos 30° + B and C<sub>y </sub>= -A sin 30°. Which statement best describes the orientation of these vectors? = Two vectors   and   , are added together to form the vector   =   +   . The relationship between the magnitudes of these vectors is given by: C<sub>x </sub>= A cos 30° + B and C<sub>y </sub>= -A sin 30°. Which statement best describes the orientation of these vectors? + Two vectors   and   , are added together to form the vector   =   +   . The relationship between the magnitudes of these vectors is given by: C<sub>x </sub>= A cos 30° + B and C<sub>y </sub>= -A sin 30°. Which statement best describes the orientation of these vectors? . The relationship between the magnitudes of these vectors is given by: Cx = A cos 30° + B and Cy = -A sin 30°. Which statement best describes the orientation of these vectors?

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A bird flies 25.0 m in the direction 55° east of south to its nest on a cliff. The bird then flies 75.0 m in the direction 55° west of north to the top of a tree. What are the northward and westward components of the resultant displacement of the bird from its nest? northward westward

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The x and y components of a displacement vector are -3.00 m and +4.00 m, respectively. What angle does this vector make with the positive x axis?

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A boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. A vector from the station to the point where the boat yxas later found is A boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. A vector from the station to the point where the boat yxas later found is  =30.0 km, 15.0° north of east. -How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector   ?=30.0 km, 15.0° north of east. -How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector A boat radioed a distress call to a Coast Guard station. At the time of the call, a vector A from the station to the boat had a magnitude of 45.0 km and was directed 15.0° east of north. A vector from the station to the point where the boat yxas later found is  =30.0 km, 15.0° north of east. -How far did the boat travel from the point where the distress call was made to the point where the boat was found? In other words, what is the magnitude of vector   ? ?

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Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are: Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? = 2.0 km, east; Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? = 5.2 km, north; Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? = 4.9 km, west; Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? = 3.0 km, south What is the resultant displacement Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? of the members of the bicycle club: Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? = Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? + Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? + Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? + Four members of the Main Street Bicycle Club meet at a certain intersection on Main Street. The members then start from the same location, but travel in different directions. A short time later, displacement vectors for the four members are:   = 2.0 km, east;   = 5.2 km, north;   = 4.9 km, west;   = 3.0 km, south What is the resultant displacement   of the members of the bicycle club:   =   +   +   +   ? ?

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A displacement vector has a magnitude of 810 m and points at an angle of 18° above the positive x axis. What are the x and y scalar components of this vector? x scalar component y scalar component

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