Q: A Cessna-172 accelerates from rest at $$a = 3.0\ \mathrm{m/s^2$} to a $$takeoff speed of $$v = 31\ \mathrm{m/s}. $$What is the minimum length of runway required for takeoff? (Assume constant acceleration.)

$$s = \frac{v^2$}{2a} = \frac{(31)^2$}{2 \times 3.0} = 160.17\ \mathrm{m}$$

Q: Solve the quadratic equation $$8x^2 + 2x - 3 = 0$ for x$.

$$x = \frac{-2 \pm \sqrt{2^2$ - 4 \times 8 \times (-3)}}{2 \times 8}$$

Q: A steel cable is used to lift an $$8,000\ \mathrm{kg}$$ load. What is the minimum tension the cable must withstand? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$T = 8,000 \times 9.8 = 78,400\ \mathrm{N}$$

Question 1

Which of the following is the most appropriate way to address your physics professor in an email, according to the course guidelines?

Accepted Answer

Dear Professor Chudnovsky,

Question 2

Galileo Galilei is known for which major contribution to physics?

Accepted Answer

Formulating the laws of motion and supporting the use of mathematics in describing nature

Question 3

A Cessna-172 accelerates from rest at $$a = 3.0\ \mathrm{m/s^2$} to a $$takeoff speed of $$v = 31\ \mathrm{m/s}. $$What is the minimum length of runway required for takeoff? (Assume constant acceleration.)

Accepted Answer

$$s = \frac{v^2$}{2a} = \frac{(31)^2$}{2 	imes 3.0} = 160.17\ \mathrm{m}$$

Question 4

Which of the following best describes the role of mathematics in physics, as emphasized by Galileo?

Accepted Answer

Mathematics is the language in which the laws of nature are written.

Question 5

Convert the fraction $$\frac{3}{7} to $$its decimal form and round to three decimal places.

Accepted Answer

$$0.429$$

Question 6

If $$x - 3 = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 8$$

Question 7

A car travels at $$55.0\ \mathrm{mi/h}$$ ($$24.6\ \mathrm{m/s}) up a $$hill. If the car's engine must overcome gravity and friction, which of the following is closest to the minimum horsepower required if the car's mass is $$1,500\ \mathrm{kg}$$ and the hill is inclined at $$10^\circ$$? (Use $$1\ \mathrm{hp} = 746\ \mathrm{W}$$, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$P = 105\ \mathrm{hp}$$

Question 8

Which of the following is the correct way to multiply powers of ten: $$(3 	imes 7) 	imes (10^2$ 	imes 10^3$)$$?

Accepted Answer

$$21 	imes 10^5$

Question 9

Solve the quadratic equation $$8x^2 + 2x - 3 = 0$ for x$.

Accepted Answer

$$x = \frac{-2 \pm \sqrt{2^2$ - 4 	imes 8 	imes (-3)}}{2 	imes 8}$$

Question 10

A steel cable is used to lift an $$8,000\ \mathrm{kg}$$ load. What is the minimum tension the cable must withstand? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$T = 8,000 	imes 9.8 = 78,400\ \mathrm{N}$$

Question 11

Which scientist is associated with the development of quantum mechanics and the uncertainty principle?

Accepted Answer

Werner Heisenberg

Question 12

If $$x = 5 - 3$$, what is the value of $$x$$?

Accepted Answer

$$x = 2$$

Question 13

Which of the following best explains why logical progress in science would be impossible without mathematics, according to Galileo?

Accepted Answer

Because mathematics allows for precise and universal expression of natural laws.

Question 14

Simplify the following expression: $$(0.42857...) 	imes 10^5$.

Accepted Answer

$$4.2857 	imes 10^4$

Question 15

Which of the following is the correct decimal representation of $$\frac{3}{13}$$ rounded to four decimal places?

Accepted Answer

$$0.2308$$

Question 16

If $$x^2 + 2x - 3 = 0$, what are the solutions for x$?

Accepted Answer

$$x = 1, x = -3$$

Question 17

Which of the following is NOT recommended when addressing your professor in person or in writing?

Accepted Answer

Hey Professor

Question 18

Which of the following best describes the relationship between physics and other natural sciences?

Accepted Answer

Physics provides the foundational basis for other natural sciences.

Question 19

If $$x - 3 = 5$$, and $$x = 8$$, what is $$2x - 3$$?

Accepted Answer

$$13$$

Introduction and Mathematical Tools for Physics 166

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