Q: A sled starts from rest at the top of a frictionless hill inclined at $$12^ ext{o} to $$the horizontal and slides $$75.0 m. $$Which equation would you use to find its final speed?

$$v^2 = 2g$$ \sin \theta \cdot d$$

Q: If the angle $$\theta of a $$vector is measured from the positive $$x-$$axis, which formula gives the direction of the vector from its components?

$$\theta = \tan$$^{-1}$$ \left( \frac{A_y}{A_x} \right)$$

Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

Given a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ measured from the positive $$x-$$axis, what is the correct expression for its $$x-$$component?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 3

If you add two vectors $$\vec{A}$$ and $$\vec{B}$$ using the tip-to-tail method, what does the resultant vector represent?

Accepted Answer

A vector pointing from the tail of $$\vec{A} to $$the tip of $$\vec{B}.$$

Question 4

What is the $$y-$$component of a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ from the positive $$x-$$axis?

Accepted Answer

$$A_y = A \sin 	heta$$

Question 5

A car moves at $$50 mi/hr at an $$angle of $$37^	ext{o}$$ south of west. Which method would you use to graphically represent its velocity vector?

Accepted Answer

Draw the vector to scale in the correct direction, using tip-to-tail addition if combining with other vectors.

Question 6

If a vector $$\vec{A} is $$multiplied by a scalar $$c = -3$$, what happens to the resulting vector?

Accepted Answer

The magnitude is tripled and the direction is reversed.

Question 7

Given vectors $$\vec{A}$$ and $$\vec{B}$$, what are the components of the vector $$\vec{C} = \vec{A} + \vec{B}$$?

Accepted Answer

$$C_x = A_x + B_x$$, $$C_y = A_y + B_y$$

Question 8

A sled starts from rest at the top of a frictionless hill inclined at $$12^	ext{o} to $$the horizontal and slides $$75.0 m. $$Which equation would you use to find its final speed?

Accepted Answer

$$v^2 = 2g$$ \sin 	heta \cdot d$$

Question 9

If the angle $$	heta of a $$vector is measured from the positive $$x-$$axis, which formula gives the direction of the vector from its components?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{A_y}{A_x} ight)$$

Question 10

Which of the following is NOT a scalar quantity?

Accepted Answer

Force

Question 11

If you subtract vector $$\vec{A}$$ from vector $$\vec{B}$$ graphically, which operation do you perform?

Accepted Answer

Add $$-\vec{A} to$$ $$\vec{B}$$ using tip-to-tail.

Question 12

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is its magnitude?

Accepted Answer

$$A = \sqrt{3^2$ + 4^2$} = 5$$

Question 13

If a vector lies in quadrant III, what adjustment must you make to the angle calculated using $$	an$$^{-1}$$?

Accepted Answer

Add $$180^	ext{o} to $$the calculator result.

Question 14

Which method can be used to add more than two vectors graphically?

Accepted Answer

Tip-to-tail method

Question 15

If you multiply a vector $$\vec{A} by a $$scalar $$c = \frac{1}{2}$$, what happens?

Accepted Answer

The magnitude is halved and the direction is unchanged.

Question 16

Which coordinate system is most convenient for analyzing motion on a ramp?

Accepted Answer

A tilted coordinate system with $$x-$$axis along the ramp and $$y-$$axis perpendicular to the ramp.

Question 17

If $$\vec{A}$$ has components $$A_x = 8$$ and $$A_y = 6$$, what is the angle $$	heta it $$makes with the positive $$x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$ \left( \frac{6}{8} ight)$$

Question 18

Which equation summarizes the addition of two vectors by components?

Accepted Answer

$$C_x = A_x + B_x$$, $$C_y = A_y + B_y$$

Vectors and Trigonometry: Vector Math and Motion on Ramps

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