Q: If a vector $$\vec{A}$$ has components $$A_x$$ and $$A_y$$, what is the angle $$\theta it $$makes with the x-axis?

$$\theta = \tan$$^{-1}$$(A_y/A_x)$$

Question 1

Which of the following statements about vectors is TRUE?

Accepted Answer

A vector has both magnitude and direction.

Question 2

Two displacement vectors, $$\vec{d}_B$$ and $$\vec{d}_S$$, have the same magnitude and direction but start at different points. What can be concluded about these vectors?

Accepted Answer

They are equal because vectors are defined by magnitude and direction only.

Question 3

A hiker walks 4 miles east and then 3 miles north. What is the magnitude of the net displacement?

Accepted Answer

$$5$$ miles

Question 4

Which rule allows you to add two vectors by placing the tail of one at the tip of the other?

Accepted Answer

Tip-to-tail rule

Question 5

If $$\vec{A} is a $$vector and $$c is a $$positive scalar, what is the result of $$c\vec{A}$$?

Accepted Answer

A vector with magnitude $$cA in $$the same direction as $$\vec{A}$$

Question 6

What happens when a vector $$\vec{A} is $$multiplied by $$-1$$?

Accepted Answer

Its direction is reversed but magnitude stays the same.

Question 7

Given a vector $$\vec{A}$$ with components $$A_x = 3$$ and $$A_y = 4$$, what is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 8

A vector $$\vec{A}$$ makes an angle $$	heta$$ with the x-axis. Which formula gives the x-component of $$\vec{A}$$?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 9

A projectile is launched with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for the horizontal component of the initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$

Question 10

A dog runs off a dock at $$8.5\ \mathrm{m/s}$$ horizontally from a height of $$0.61\ \mathrm{m}. $$How far from the dock does the dog land? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.4\ \mathrm{m}$$

Question 11

Which of the following is TRUE about projectile motion (neglecting air resistance)?

Accepted Answer

The horizontal acceleration is zero and the vertical acceleration is $$-g.$$

Question 12

A soccer ball is kicked at $$23\ \mathrm{m/s} at an $$angle of $$22^\circ$$ above the horizontal. How long does it take to reach a goal $$18\ \mathrm{m}$$ away?

Accepted Answer

$$0.77\ \mathrm{s}$$

Question 13

Which launch angle gives the maximum range for a projectile (neglecting air resistance)?

Accepted Answer

$$45^\circ$$

Question 14

A rock is launched at $$5\ \mathrm{m/s} at$$ $$50^\circ$$ above the ground. What is the total time of flight? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$0.78\ \mathrm{s}$$

Question 15

A vector has components $$A_x = -5.2\ \mathrm{m/s^2$}$$ and $$A_y = -3.0\ \mathrm{m/s^2$}. $$What is the magnitude of the vector?

Accepted Answer

$$6.0\ \mathrm{m/s^2$}$$

Question 16

Which of the following best describes the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

It is always downward with magnitude $$g.$$

Question 17

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

Accepted Answer

$$	heta = 	an$$^{-1}$$(A_y/A_x)$$

Question 18

A projectile is launched and lands at the same height. Which of the following is TRUE about its vertical velocity at launch and landing?

Accepted Answer

The vertical velocity at landing is equal in magnitude and opposite in direction to the launch velocity.

Question 19

Which of the following is NOT a property of the zero vector?

Accepted Answer

It has a negative magnitude.

Vectors and Motion in Two Dimensions: Study Notes for Physics with Algebra

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