Q: A projectile is launched from the ground with an initial velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. Which formula gives the time to reach maximum height?

$$t = \frac{v_0$ \sin \theta}{g}$$

Q: A vector $$\vec{v}$$ has components $$v_x = -5$$ and $$v_y = 12. $$What is the angle $$\theta it $$makes with the positive $$x-$$axis?

$$\theta = \tan$$^{-1}$$\left(\frac{12}{-5}\right)$$

Q: Which of the following is true about the dot product of two vectors $$\vec{a}$$ and $$\vec{b}$$?

$$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta$$

Question 1

A car travels 1200 meters in 3 minutes. What is its average speed in meters per second ($$\frac{m}{s}$$)?

Accepted Answer

$$6.67\ \frac{m}{s}$$

Question 2

Given a vector $$\vec{v} = 3\hat{i} + 4\hat{j}$$, what is its magnitude?

Accepted Answer

$$5$$

Question 3

If $$\vec{a} = 2\hat{i} + 3\hat{j}$$ and $$\vec{b} = 4\hat{i} - \hat{j}$$, what is the dot product $$\vec{a} \cdot \vec{b}$$?

Accepted Answer

$$11$$

Question 4

A projectile is launched from the ground with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. Which formula gives the time to reach maximum height?

Accepted Answer

$$t = \frac{v_0$ \sin 	heta}{g}$$

Question 5

Which of the following correctly expresses the displacement vector $$\Delta \vec{r}$$ between two points $$\vec{r}_1$$ and $$\vec{r}_2$$?

Accepted Answer

$$\Delta \vec{r} = \vec{r}_2 - \vec{r}_1$$

Question 6

A ball is thrown vertically upward with initial velocity $$v_0. $$What is its velocity after time $$t$$? (Assume upward is positive and acceleration due to gravity is $$-g.)$$

Accepted Answer

$$v = v_0$ - gt$$

Question 7

A vector $$\vec{v}$$ has components $$v_x = -5$$ and $$v_y = 12. $$What is the angle $$	heta it $$makes with the positive $$x-$$axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{12}{-5}ight)$$

Question 8

Which of the following statements about the projection of a vector onto an axis is correct?

Accepted Answer

The projection equals the magnitude of the vector times the cosine of the angle between the vector and the axis.

Question 9

A projectile is fired horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 10

If a vector $$\vec{A}$$ has components $$A_x = 0$$ and $$A_y = 0$$, what can be said about its direction?

Accepted Answer

The direction is undefined.

Question 11

A ball collides elastically with a vertical wall at $$x = x_k. $$Which component of its velocity changes sign after the collision?

Accepted Answer

The $$x-$$component

Question 12

Which formula gives the position $$x of a $$particle moving with constant acceleration $$a$$ after time $$t$$, starting from $$x_0$$ with initial velocity $$v_0$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 13

A vector $$\vec{v} is $$specified by its Cartesian components $$v_x$$ and $$v_y. $$What is the formula for its magnitude?

Accepted Answer

$$|\vec{v}| = \sqrt{v_x^2$ + v_y^2$}$$

Question 14

A projectile passes through the point $$(x_0$, y_0$). $$Which condition must be satisfied at that instant?

Accepted Answer

$$x = x_0$,\ y = y_0$

Question 15

Which equation describes the velocity of a particle as the derivative of its position vector with respect to time?

Accepted Answer

$$\vec{v} = \frac{d\vec{r}}{dt}$$

Question 16

A vector $$\vec{A} is $$projected onto the $$y-$$axis. If the angle between $$\vec{A}$$ and the $$y-$$axis is $$	heta$$, what is the projection?

Accepted Answer

$$|\vec{A}| \cos 	heta$$

Question 17

Which of the following is true about the dot product of two vectors $$\vec{a}$$ and $$\vec{b}$$?

Accepted Answer

$$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 	heta$$

Question 18

A ball collides with a horizontal surface at $$y = y_k. $$Which component of its velocity changes sign after the collision?

Accepted Answer

The $$y-$$component

Question 19

If a vector is measured with respect to the negative direction along an axis, what must be done to its projection?

Accepted Answer

A negative sign must be included in front of the projection.

Fundamental Concepts in Physics: Unit Conversions, Vectors, and Kinematics

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