Scalar quantities have only magnitude (amount) ex. time, temperature distance
Vector quantities have magnitude and direction ex.
We represent them as arrows
Distance (d): how far an object has moved.
Is distance a scalar or a vector? scalar_____
Displacement $ (\vec{d})$ : change in position.
Is displacement a scalar or a vector?vecter____
Ex: A student walks $5 \mathrm{~m}$ east and then $3 \mathrm{~m}$ west.
Ex: A polar bear meanders $275 \mathrm{~m}$ east and then turns around and ambles $425 \mathrm{~m}$ west.
Ex: A student walks $5 \mathrm{~m}$ east and then $3 \mathrm{~m}$ west.
a) What is the distance (scalar) travelled?
$d_T=d_1+d_2=5+3=8 \mathrm{~m}$
b) What is the student’s displacement (vector)?
$\vec{d}_T=\vec{d}_1+\vec{d}_2$
$\vec{d}_T$
$\vec{d}_T=2 m$ East
NOTE: When adding Vectors… USe the tip to tail method
Ex: A polar bear meanders $275 \mathrm{~m}$ east and then turns around and ambles $425 \mathrm{~m}$ west.
a) What was the distance travelled by the bear?
$\begin{aligned} d_\tau=d_1+d_2 & =275+425 \\ & =700 \mathrm{~m}\end{aligned}$
b) What was the bear’s displacement?
$\vec{d}_t=\quad 275 \mathrm{~m}$
$\begin{aligned} \vec{d} & =\vec{d}_1+\vec{d}_2 \\ & =(275)+(-425) \\ & =-150 \mathrm{~m}\end{aligned}$
Ex: A little girl takes her dog for a walk around a city block as shown.
a) What is the distance travelled?
$\begin{aligned} d_{T} & =11 5+12 5+11 5+12 5 \\ & =480 m\end{aligned}$
b) What is her final displacement?
$\vec{d}_T=0 m$
c) What was her displacement at B?
$\vec{d}_T$ resultant vecter
$\begin{aligned} d_T^2 & =115^2+125^2 \\ d_T & =\sqrt{115^2+125^2} \\ & =169.85 \\ & =170 \mathrm{m}\end{aligned}$
$\begin{aligned} & \tan \theta=\frac{125}{115} \\ & \theta=\tan ^{-1}\left(\frac{125}{45}\right) \\ & =47^{\circ} \end{aligned}$
$170 . \mathrm{m}$ $47^{\circ}$ $\mathrm{S}$ of $\mathrm{E}$
Describe the following angles
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