91影视

A wheel with a radius of 45.0 cmrolls without slipping along a horizontal floor (Fig). At time t, the dot P painted on the rim of the wheel is at the point of contact between the wheel and the floor. At a later time t₂, the wheel has rolled through one-half of a revolution. What are (a) the magnitude and (b) the angle (relative to the floor) of the displacement of P?

In Fig.$\mathbf{3}\mathbf{-}\mathbf{27}$, a heavy piece of machinery is raised by sliding it a distance$\mathit{d}\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{m}$along a plank oriented at angle$\mathit{胃}\mathbf{=}\mathbf{20}\mathbf{.}\mathbf{0}\mathbf{掳}$to the horizontal. How far is it moved (a) vertically and (b) horizontally?

Describe two vectors$\stackrel{\mathbf{鈬赌}}{\mathbf{a}}\mathbf{}\mathbf{and}\mathbf{}\stackrel{\mathbf{鈬赌}}{\mathbf{b}}$such that

$$\begin{gathered} \mathbf{a}\mathbf{)}\mathbf{}\mathbf{}\stackrel{\mathbf{鈬赌}}{\mathbf{a}}\mathbf{+}\stackrel{\mathbf{鈬赌}}{\mathbf{b}}\mathbf{=}\stackrel{\mathbf{鈬赌}}{\mathbf{c}}\mathbf{}\mathbf{and}\mathbf{}\mathbf{a}\mathbf{+}\mathbf{b}\mathbf{=}\mathbf{c}\mathbf{;} \\ \mathbf{b}\mathbf{)}\mathbf{}\mathbf{}\stackrel{\mathbf{鈬赌}}{\mathbf{a}}\mathbf{+}\stackrel{\mathbf{鈬赌}}{\mathbf{b}}\mathbf{=}\stackrel{\mathbf{鈬赌}}{\mathbf{a}}\mathbf{-}\stackrel{\mathbf{鈬赌}}{\mathbf{b}}\mathbf{;} \\ \mathbf{c}\mathbf{)}\mathbf{}\mathbf{}\stackrel{\mathbf{鈬赌}}{\mathbf{a}}\mathbf{+}\stackrel{\mathbf{鈬赌}}{\mathbf{b}}\mathbf{=}\stackrel{\mathbf{鈬赌}}{\mathbf{c}}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{+}{\mathbf{b}}^{\mathbf{2}}\mathbf{=}{\mathbf{c}}^{\mathbf{2}} \end{gathered}$$

A woman walksin the direction$\mathbf{30}\mathbf{掳}$east of north, then$\mathbf{175}\mathbf{}\mathbf{m}$directly east. Find (a) the magnitude and (b) the angle of her final displacement from the starting point. (c) Find the distance she walks. (d) Which is greater, that distance or the magnitude of her displacement?

A vector $\stackrel{\mathbf{鈫�}}{\mathbf{d}}$has a magnitude 3.0 m and is directed south. Whatare (a) the magnitude and (b) the direction of the vector$\mathbf{5}\mathbf{.}\mathbf{0}\stackrel{\mathbf{鈫�}}{\mathbf{d}}$? Whatare (c) the magnitude and (d) the direction of the vector $\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{0}\stackrel{\mathbf{鈫�}}{\mathbf{d}}$?

A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: $\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{1}}}$for 0.40 msouthwest (that is, at $\mathbf{45}\mathbf{掳}$from directly south and from directly west),$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{2}}}$for 0.50 mdue east,$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{3}}}$for 0.60 mat$\mathbf{60}\mathbf{掳}$north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{1}}}$? Next, what are (c) the x component and (d) the y component of$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{2}}}$? Also, what are (e) the x component and (f) the y component of$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{3}}}$?

What are (g) the x component, (h) the y component, (i) the magnitude, and (j) the direction of the ant鈥檚 net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move?

Two vectors are given by $\mathbf{a}\mathbf{}\mathbf{鈨�}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{0}\hat{\mathbf{i}}\mathbf{+}\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\hat{\mathbf{j}}\mathbf{}\mathbf{and}\mathbf{}\mathbf{b}\mathbf{}\mathbf{鈨�}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{0}\hat{\mathbf{i}}\mathbf{}\mathbf{4}\mathbf{.}\mathbf{0}\hat{\mathbf{j}}$. Find localid="1656307855911" $\mathbf{\left(}\mathbf{a}\mathbf{\right)}\mathbf{}\mathbf{a}\mathbf{}\mathbf{鈨�}\mathbf{脳}\mathbf{b}\mathbf{}\mathbf{鈨�}\mathbf{,}\mathbf{}\mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathbf{}\mathbf{a}\mathbf{}\mathbf{鈨�}\mathbf{鈰�}\mathbf{b}\mathbf{}\mathbf{鈨�}\mathbf{,}\mathbf{}\mathbf{\left(}\mathbf{c}\mathbf{\right)}\mathbf{}\mathbf{(}\mathbf{a}\mathbf{}\mathbf{鈨�}\mathbf{+}\mathbf{b}\mathbf{}\mathbf{鈨�}\mathbf{}\mathbf{)}\mathbf{鈰�}\mathbf{b}\mathbf{}\mathbf{鈨�}\mathbf{,}\mathbf{}$and (d) the component of $\stackrel{\mathbf{鈫�}}{\mathbf{a}}$along the direction of $\stackrel{\mathbf{鈫�}}{\mathbf{b}}$.

Vector $\stackrel{\mathbf{鈫�}}{\mathbf{a}}$lies in the yz plane $\mathbf{63}\mathbf{.}\mathbf{0}\mathbf{掳}$from the positive direction of the y axis, has a positive z component, and has magnitude 3.20units. Vector $\stackrel{\mathbf{鈫�}}{\mathit{b}}$lies in xz the plane 48.0from the positive direction of the x axis, has a positive z component, and has magnitude$\mathbf{1}\mathbf{.}\mathbf{40}\mathbf{掳}$units. Find (a)role="math" localid="1661144136421" $\stackrel{\mathbf{鈫�}}{\mathbf{a}}路\stackrel{\mathbf{鈫�}}{\mathbf{b}}$, (b)$\stackrel{\mathbf{鈫�}}{\mathbf{a}}\mathbf{脳}\stackrel{\mathbf{鈫�}}{\mathbf{b}}$, and (c) the angle between$\stackrel{\mathbf{鈫�}}{\mathbf{a}}$and$\stackrel{\mathbf{鈫�}}{\mathbf{b}}$.

Find (a) 鈥渘orth cross west,鈥� (b) 鈥渄own dot south,鈥� (c) 鈥渆ast cross up,鈥� (d) 鈥渨est dot west,鈥� and (e) 鈥渟outh cross south.鈥� Let each 鈥渧ector鈥� have unit magnitude

A vector$\stackrel{\mathbf{鈬赌}}{\mathbf{B}}$, with a magnitude of$\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}$, is added to a vector $\stackrel{\mathbf{鈬赌}}{\mathbf{A}}$, which lies along an x axis. The sum of these two vectors is a third vector that lies along the y axis and has a magnitude that is twice the magnitude of$\stackrel{\mathbf{鈬赌}}{\mathbf{A}}$. What is the magnitude of $\stackrel{\mathbf{鈬赌}}{\mathbf{A}}$?