LAB 1 Review of Algebra and Trigonometry

(Points possible: 10) Only submit Pages 3 - 6 of this document for grading along with your cover sheet. One point will be deducted for loose pages. One point will be deducted if cover sheet is missing.

Algebra Review

1. Solving an equation for x: Look at exponents on x, then choose from: (1) All xexponents and no x2-terms (linear equation)

i. Add or subtract from both sides to get all terms containing x on one side of the equal sign and all other terms on the other side.

ii. Factor out an x from the side with xterms if necessary iii. Divide both sides by what multiples x iv. Simplify if possible

(2) There are x2terms but no xterms (quadratic equation): i. Solve for x2 using above method ii. Take square root of both sides

(3) There are both x2-terms and xterms (also quadratic equation) i. Rearrange into form ax2 + bx + c = 0 (Very Important!) ii. Use the quadratic formula: iii. If two answers result from , choose answer that makes physical sense (e.g. distance and time are not usually negative)

2. Parenthesis

Example: Use a = 15, b = 3, t = 4, solve each equation for x (1) x = (a b) / t Solution: x = (15 3) / 4 x = 12 / 4 x = 3

(2) x = (2(a b) + 3b 5) / (t + b) Solution: x = (2 (15 3) + 3(3) 5) / (4 + 3) x = (2 (12) + 9 5) / 7 x = 4

(3) x = 2(a b)2 / 10 Solution: x = 2 (15 3) 2 / 10 x = 2 (12) 2 / 10 x = 2 (144) / 10 x = 28.8

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3. Exponentials (squares, square roots, etc.)

Examples: Use the following formula to compute the desired quantity: d = v t + 0.5 at2

(1) If v = 5, t = 2, a = 10; what is d? Solution: d = 5(2) + 0.5(10)(2) 2 d = 10 + (5)(4) d = 30

(2) If d = 80, t = 2, a = 10; what is v? Solution: d = v t + 0.5 at2 v t = d 0.5 at2 v = (d 0.5 at2) / t v = (80 0.5(10)(22)) / 2 v = (80 20) / 2 v = 60 / 20 v = 3

Trigonometry Review

Definitions:

Right (angle) triangle: a triangle containing an internal right angle (90). Acute angles: angles smaller than 90 Obtuse angles: angles greater 90

A right triangle has three and angles three sides as shown below:

Hypotenuse: the longest side opposite to the right angle Opposite: the side opposite to the angle of your interest Adjacent: the side between the right angle and the angle of your interest

You can also use SOH CAH TOA strategy:

SOH = Sine of the angle = Opposite side / Hypotenuse CAH = Cosine of the angle = Adjacent side / Hypotenuse TOA = Tangent of the angle = Opposite side / Adjacent side

If you want to compute the internal angle of your interest from the known sides of a right angle triangle, you can use inverse of trigonometric properties: arc sine (ARCSIN; sin1), arc cosine (ARCCOS; cos1), and arc tangent (ARCTAN; tan1) functions.

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Solve the following questions; show all the steps in the space provided, and write encircle the final answer.

PART A: Review of Algebra (0.5 points each, no partial grading)

1. If v=u+at; a=9.8; t=3; u=0, Calculate v. 2. Solve for x : 5x 1 = 3(x + 3)

3. Solve for x: 5(x+2) + 2x = 5 x

4. Solve for y: 2y2 5y 3 = 0

5. d = 0.5(at2) Solve for t in terms of a and d

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Review of Trigonometry (0.5 points each, no partial grading) 6. Given the hypotenuse = 10 m, angle = 45, find the lengths of both adjacent and opposite sides.

7. Given the hypotenuse = 4 m, side A = 3 m, find both acute angles.

8. Ronaldo kicked a soccer ball into the air at an angle of 45 to the horizontal with an initial resultant velocity of 30 m/s. Find both the vertical and horizontal components of the velocity vector. Hint: the angle of your interest is 45 and you want to find adjacent and opposite lengths with the given hypotenuse 30 m/s.

9. What is the course policy with regards to late submission of lab reports?

10. What is your TAs name and lab section number? (You have to remember your section

number for exams)

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11) The velocity of which a diver hits the surface of the water is given by the equation: mv2 = mgh Where m = mass of the diver

g = acceleration due to gravity h = height from which the person dives

a) [0.5 points] Write down the velocity in terms of other variables i.e. Solve the equation for

velocity b) [0.5 points] Find the velocity at the surface if the person jumps from a height of 10m

12) [1 point] A ball is thrown vertically upwards in the air at a velocity of 50 m/s and reaches a

maximum height of 127.42 m. Calculate the time when the ball reaches the 10 m mark, while going up and coming down. Use the following equation of motion:

yf = yi + vit + at2 where yf and yi are final and initial position, vi is initial velocity, a is

acceleration and t is time, respectively. 13) A runner starts from point A and runs 50m at an angle of 60 to the horizontal and then

covers a displacement of 50m at an angle 30 to the horizontal to reach point C.

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a. [1 point] Find the horizontal displacement between A and B, and B and C.

b. [1 point] Find the vertical displacement between A and B, and B and C.

14) [1 point] When a person steps on the ground, the weight of the person pushes the floor with

some force. According to Newtons third law, the ground pushes the person back with an equal and opposite force. If the person weighs 900 N, find the vertical component of the ground reaction force if the weight of the person acts as shown in the figure.

900 N

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LAB 1Algebra Reviewi. Rearrange into form ax2 + bx + c = 0 (Very Important!)

2. Parenthesis3. Exponentials (squares, square roots, etc.)Trigonometry ReviewDefinitions:

Solve the following questions; show all the steps in the space provided, and write encircle the final answer.