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Quiz 13
1. Vector or scalar?
a.) $25 \dfrac{\mathrm{miles}}{\mathrm{hour}}$
b.) $25 \dfrac{\mathrm{miles}}{\mathrm{hour}}$ north
Solution: For a.), it is a scalar (it has no direction). For b.), it is a vector because it has a magnitude (the speed) and a direction (north).
2. Sketch the resultant $\vec{x}+\vec{y}$ where $\vec{x}=$
and $\vec{y}=$
.
Solution: Calculate
$\vec{x}+\vec{y}=$
3. Sketch the resultant of $2\vec{x}-\vec{y}$ where $\vec{x}=$
and $\vec{y}=$
.
Solution: Here, $2\vec{x}=$
and $-\vec{y}=$
. So,
$2\vec{x}-\vec{y}=2\vec{x}+(-\vec{y})=$
4. Find the components of the vector that is drawn:
Solution: By the definition of cosine, $\cos(10^{\circ})=\dfrac{x}{3}$, or in other words,
$$x=3\cos(10^{\circ})=2.954$$
and the definition of sine gives $\sin(10^{\circ})=\dfrac{y}{3}$, or in other words,
$$y=3\sin(10^{\circ})=0.5209.$$
5. Find the components of the vector that is drawn:
Solution: Here both the $x$-component and $y$-component are negative. The reference angle of $205^{\circ}$ is $205^{\circ}-180^{\circ}=25^{\circ}$. So
$$x=-117\cos(25^{\circ})=-106,$$
and
$$y=-117\sin(25^{\circ})=-49.45.$$
