Ocean City High School HONORS PHYSICS Summer Enrichment Assignment 2015

Transcription

1 Ocean City High School HONORS PHYSICS Summer Enrichment Assignment 2015 Course: Honors Physics (11 th / th ) Teachers: duhrich@ocsdnj.org, dweaver@ocsdnj.org, Due Date: Mr. Uhrich Mr. Weaver First Day of Class Standards Topic Purpose NJCCCS: 5.1..A.2, 5.1..B.2, 5.1..D.2 Mathematical Review/Introduction Serve as the foundation for our rigorous course of study by providing a mathematical review that will help you brush up on the mathematical concepts utilized throughout the course Tet/Novel(s) & Brief Description This packet and internet resources (if needed) Mr. Uhrich s Summer Assignment Website: Approimate Time on Task 3-4 hrs Suggested Timeline How It Will Be Assessed Completed in full prior to 1 st day of school This enrichment activity will not receive a score directly, however math skills from this packet will be quickly reviewed as needed in the general content of the course. Students will need to apply these math skills in the contet of each unit. Please complete the following problems in the space provided. Show all work. Every answer must be complete and correct. There will be a quiz within the first week of school. B. Solve for all possible values of Part One: Algebra 1.) 3 7 = 8 2.) = 24

2 3.) ½ + 5 = 11 6.) = 0 4.) 2 +3 = 5 7.) ( +3)/2 = 4 5.) 2 6 = 0 B. Solve for each bold and underlined variable in terms of the other variables Eample: Solve for. (2 + y) = z = z 2 + y 8.) F = ma 10.) ½ m v 2 = mgh 9.) v = v o + at 11.) = ½ a t 2

3 C. Solve for all variables.) + y = 7 y = 3 15.) 2 2y = y = 30 (Two sets of answers!) 13.) 7 5 = y 15 = 3 + 5y 16.) 5 + 6y + z = 20 3y 7z = -35 y + z = 5 14.) sin(30) + sin(50)y = 90 cos(30) cos(50)y = 0

4 Part Two: Conversion Factor Practice Step 1: Write whatever you are trying to convert as a fraction. For instance, you can write 60 mph as 60 miles/1 hour. If the unit can't be written as a fraction, simply place the unit over 1 as a placeholer, for eample 300 ft / 1. Step 2: Determine what units you want to end with. Step 3: Any unit that you start with that you do not want to end with needs to be cancelled. In order to cancel unwanted units, you must multiply by conversion factors. Conversion factors are a fraction that show the conversion rate between two units (For eample inches / 1 foot). Because the numerator and denominator are equal, the fraction is equal to one, and thus can be multiplied without changing the initial value. Also, because the numerator and denominator are equal, conversion factors can be flipped ( inches / 1 foot can also be written as 1 foot / inches). In order to cancel unwanted units, simply place the unwanted unit on the opposite side of the fraction in your conversion factor. For eample, if you want to get rid of "miles" in your numerator, your conversion factor should have "miles" in the denominator. Step 4: Continue using conversion factors until all unwanted units are cancelled. Step 5: Multiply as you would with fractions, multiplying across your numerators, then dividing by all numbers in your denominators. Eample #1: Convert 1.75 miles into feet 1.75 miles 5280 feet = 9240 feet 1 1 mile Eample #2: Convert 60 mph into ft/s 60 miles 5280 feet 1 hour 1 minute = feet = 88 ft/s 1 hour 1 mile 60 minutes 60 seconds 3600 seconds Problems: Perform the following conversions. Show all work! 1. Convert 300 yards into miles (There are 3 feet in a yard, and 5280 feet in a mile).

5 2. How many inches are in a marathon? (26.2 miles in a marathon, 5280 feet in a mile) 3. How many seconds are in one year (assuming it is not a leap year)? 4. Convert 25 mph into feet per second 5. Convert 65 mph into meters per second (There are 1.61 km in a mile, and 1000 m in a km). 6. Convert 16.7 grams into kilograms (there are 1000g in 1 kg).

6 Part Three: Trigonometry We will be working with the sine, cosine, and tangent functions in this course. While not everyone has come across these terms in math class yet, we will be introducing the basics in this packet. You will need a calculator with these functions for the course. They are defined for right triangles as follows: Opposite sin Hypotenuse adjacent cos hypotenuse opposite hypotenuse opposite tan adjacent adjacent These relationships can be remembered with the pneumonic device, SOH CAH TOA. Eamples : Use the trigonometric functions to find the missing lengths for the following triangles. E 1. E Look at the triangle and identify which sides you have. The side with a value of 5 is opposite of the 30 degree angle. The side with the value of is the hypotenuse. Now select the trigonometric function that relates the opposite side and the hypotenuse. Opposite sin Hypotenuse For this triangle the sides are the adjacent side and the hypotenuse. Therefore, we use the cosine function. cos 40 cos 40 E sin 30 Solve this equation for. sin sin tan25 = tan25 = =5.6 25

7 This is how we use the trigonometric functions to find the length of the sides of a right triangle. We can also use it to find the angles in a triangle. Eamples Find the value for the angle,, in each of the following problems. E 4. Identify the sides that are known. In this problem we know the side that is opposite of and the hypotenuse. This means that we choose the sine function. 8 8 sin= In order to solve this equation, we must use the inverse trigonometric functions. We take the inverse sine (sin -1 ) of both sides of the equation sin (sin)=sin ( ) =42 PROBLEMS 1. Find the value of and the length of the missing side of the triangle Find the value of. 2 8

8 3. Solve for and missing side of triangle Solve for c and the missing side of triangle. c Solve for and the hypotenuse Solve for

9 Part Four: Graphical Analysis You should be familiar with graph construction (by hand and on Ecel). This is a topic that often shows up in the course Note: When you are told to graph Apples vs. Oranges, the 1st thing goes on the y-ais. The 2nd thing is on the -ais. 1) Use the table above to plot the points on the grid below as position vs time. Scale your ais so that you fill the available space with your graph. Be sure to correctly label the graph (aes labels, including units, scale, and title) Time, t (sec.) Position, (meters) ) Draw in the best fit line through your data points using a ruler. 3) Now use Ecel to plot the graph on the computer. Record the equation of the best-fit line and R 2 value here. Basics or (Attach Ecel graph to this packet) 4) What is the slope of the line that you plotted (with correct units)?