Exam 1: Introduction and Vectors

Which of the following products of ratios gives the conversion factors to convert meters per second $\left( \frac { \mathrm { m } } { \mathrm { s } } \right)$ to miles per hour $\left( \frac { \mathrm { mi } } { \mathrm { h } } \right)$ ?

Exhibit 3-2 A child starts at one corner of a cubical jungle gym in a playground and climbs up to the diagonally opposite corner.The original corner is the coordinate origin,and the x,y and z axes are oriented along the jungle gym edges.The length of each side is 2 m. Use this exhibit to answer the following question(s). -Refer to Exhibit 3-2.The child's displacement is:

A vector starts at coordinate (3.0,4.0)and ends at coordinate (-2.0,16.0).What are the magnitude and direction of this vector?

Which of the following products of ratios gives the conversion factor to convert miles per hour $\left( \frac { \mathrm { mi } } { \mathrm { h } } \right)$ to meters per second $\left( \frac { \mathrm { m } } { \mathrm { s } } \right)$ ?

Starting from one oasis,a camel walks 25 km in a direction 30 $\degree$ south of west and then walks 30 km toward the north to a second oasis.What distance separates the two oases?

The equation for the change of position of a train starting at x = 0 m is given by $x = \frac { 1 } { 2 } a t ^ { 2 } + b t ^ { 3 }$ .The dimensions of b are

If vector $\overrightarrow { \mathrm { C } }$ is added to vector $\overrightarrow { \mathrm { D } }$ ,the result is a third vector that is perpendicular to $\overrightarrow { \mathrm { D } }$ and has a magnitude equal to 3 $\overrightarrow { \mathrm { D } }$ .What is the ratio of the magnitude of $\overrightarrow { \mathrm { C } }$ to that of $\overrightarrow { \mathrm { D } }$ ?

The vector $\overrightarrow { \mathrm { A } }$ has components +5 and +7 along the x and y axes respectively.If the vector is now rotated 90 degrees counterclockwise relative to the original axes,the vector's components are now

Vectors $\overrightarrow { \mathrm { A } }$ and $\vec { B }$ have equal magnitudes.Which statement is always true?

Given that $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } } = x _ { 2 } \hat { \mathbf { i } } + y _ { 2 } \hat { \mathbf { j } }$ ,what is $\overrightarrow { \mathrm { A } }$ ?

If you drove day and night without stopping for one year without exceeding the legal highway speed limit in the United States,the maximum number of miles you could drive would be closest to:

The answer to a question is [MLT ^{- 1}].The question is "What are the dimensions of

Exhibit 3-1 The three forces shown act on a particle. Use this exhibit to answer the following question(s).. -Refer to Exhibit 3-1.What is the direction of the resultant of these three forces?

The rectangular coordinates of a point are (5.00,y)and the polar coordinates of this point are (r,67.4°).What is the value of the polar coordinate r in this case?

If vector $\vec { B }$ is added to vector $\overrightarrow { \mathrm { A } }$ ,the result is $6 \tilde { \mathbf { i } } + \hat { \mathbf { j } }$ .If $\vec { B }$ is subtracted from $\overrightarrow { \mathrm { A } }$ ,the result is $- 4 \tilde { \mathbf { i } } + 7 \tilde { \mathbf { j } }$ .What is the magnitude of $\overrightarrow { \mathrm { A } }$ ?

Given that $\overrightarrow { \mathbf { A } } + 2 \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$ and $2 \overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } } = x _ { 2 } \hat { \mathbf { i } } + y _ { 2 } \hat { \mathbf { j } }$ ,what is $\overrightarrow { \mathrm { A } }$ ?

If $\overrightarrow { \mathbf { A } } = 12 \hat { \mathbf { i } } - 16 \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { B } } = - 24 \hat { \mathbf { i } } + 10 \hat { \mathbf { j } }$ ,what is the direction of the vector $\overrightarrow { \mathrm { C } } = 2 \overrightarrow { \mathrm { A } } - \overrightarrow { \mathrm { B } }$ ?

Given that $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } } = x _ { 2 } \hat { \mathbf { i } } + y _ { 2 } \hat { \mathbf { j } }$ ,what is $\vec { B }$ ?

What is the mass of air in a room that measures 5.0 m * 8.0 m * 3.0 m? (The density of air is 1/800 that of water).

Find the average density of a white dwarf star if it has a mass equal to that of the sun (2.0 * 10³⁰ kg)and a radius equal to that of the Earth (6.4*10⁶ m).