Q: A building casts a shadow of 67.2 m on a sunny day. If the angle between the sun’s rays and the ground is $$50.0^\circ$$, what is the height of the building?

$$h = 67.2 \times \tan(50.0^\circ)$$

Q: Which trigonometric function relates the opposite side and adjacent side of a right triangle?

$$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$$

Q: A person leans a ladder against a wall, making an angle $$\theta$$ with the ground. If the ladder is 10 m long and the angle is $$60^\circ$$, what is the height $$h$$ above the ground where the ladder touches the wall?

$$h = 10 \times \sin(60^\circ)$$

Q: If $$\tan \theta = 1.19$$, what is $$\theta in $$degrees?

$$\theta = \tan$$^{-1}$$(1.19) \approx 50.0^\circ$$

Question 1

Which of the following best describes the purpose of dimensional analysis in physics?

Accepted Answer

To check the consistency of equations by ensuring both sides have the same dimensions

Question 2

Given the equation $$v = at + \frac{1}{2} a t^2$, what are the dimensions of a$ (acceleration)?

Accepted Answer

$$[L][T]^{-2}$$

Question 3

A building casts a shadow of 67.2 m on a sunny day. If the angle between the sun’s rays and the ground is $$50.0^\circ$$, what is the height of the building?

Accepted Answer

$$h = 67.2 	imes 	an(50.0^\circ)$$

Question 4

Which equation correctly represents the Pythagorean theorem for a right triangle?

Accepted Answer

$$p^2$$ = $$b^2$$ + $$h^2$$

Question 5

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

Accepted Answer

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

Question 6

Which of the following is true about the addition of opposite vectors $$\vec{A}$$ and $$-\vec{A}$$?

Accepted Answer

Their sum is the zero vector

Question 7

A vector $$\vec{B} is $$multiplied by $$-1. $$What happens to its magnitude and direction?

Accepted Answer

Magnitude is unchanged, direction is reversed

Question 8

If two vectors are perpendicular, what is the angle between them?

Accepted Answer

$$90^\circ$$

Question 9

Which trigonometric function relates the opposite side and adjacent side of a right triangle?

Accepted Answer

$$	an 	heta = \frac{	ext{opposite}}{	ext{adjacent}}$$

Question 10

A person leans a ladder against a wall, making an angle $$	heta$$ with the ground. If the ladder is 10 m long and the angle is $$60^\circ$$, what is the height $$h$$ above the ground where the ladder touches the wall?

Accepted Answer

$$h = 10 	imes \sin(60^\circ)$$

Question 11

Which of the following is the correct dimensional formula for velocity?

Accepted Answer

$$[L][T]^{-1}$$

Question 12

If $$\vec{A}$$ and $$\vec{B}$$ are two vectors, which graphical method can be used to find their resultant?

Accepted Answer

Head-to-tail method

Question 13

A vector $$\vec{F}$$ has components $$F_x$$ and $$F_y. $$Which equation gives the magnitude of $$\vec{F}$$?

Accepted Answer

$$|\vec{F}| = \sqrt{F_x^2$ + F_y^2$}$$

Question 14

Which of the following is NOT a valid unit for acceleration?

Accepted Answer

$$	ext{kg/s}^2$$

Question 15

If $$\vec{A}$$ and $$\vec{B}$$ are collinear and in the same direction, what is the magnitude of their resultant?

Accepted Answer

$$|\vec{A}| + |\vec{B}|$$

Question 16

Which prefix represents $$10^{-3} in $$the metric system?

Accepted Answer

milli

Question 17

A vector $$\vec{R} is $$the diagonal of a parallelogram formed by vectors $$\vec{A}$$ and $$\vec{B}. $$What does $$\vec{R}$$ represent?

Accepted Answer

The resultant of $$\vec{A}$$ and $$\vec{B}$$

Question 18

Which of the following equations is dimensionally consistent for time $$t$$?

Accepted Answer

$$t = \sqrt{\frac{2x}{a}}$$

Question 19

If $$	an 	heta = 1.19$$, what is $$	heta in $$degrees?

Accepted Answer

$$	heta = 	an$$^{-1}$$(1.19) \approx 50.0^\circ$$

Chapter 1: Introduction and Mathematical Concepts – College Physics Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards