 Given a right triangle with acute angle θ: θ

 For the given triangle, calculate sine, cosine, and tangent: θ

 Make sure your calculator is set to degree mode (not radian mode)  Test:  Type in sin(30)  If you get 0.5, then you are in degree mode  If you get anything else, then you are in a different mode and need to switch to degree mode

 A component of a vector is its projection onto an axis (x-axis or y-axis).

 A small airplane leaves an airport on an overcast day and is later sighted 215 km away, in a direction making an angle of 22° east of north. How far east and north is the airplane from the airport when sighted?

 A rocket is launched at an angle of 70.° above horizontal at 125 m/s.  How fast is it traveling horizontally?  How fast is it traveling vertically?

 A 45 kg box is moving on frictionless ice. Jon is pushing it east with a force of 75 N, while Roger is pushing it north with a force of 12 N.  What is the magnitude and direction of the net force on the box?

 A car drives 25 miles east and 60. miles north.  What is the direction and magnitude of the car’s displacement?

 A unit vector is a vector with magnitude of exactly 1.  The sole purpose of a unit vector is to specify a direction.  The unit vector in the positive x direction is  The unit vector in the positive y direction is

 To add vectors:  add the x-components  add the y-components

 A baseball is hit at an angle of 37° above horizontal at 15 m/s.  How fast is it traveling horizontally?  How fast is it traveling vertically?

 In projectile motion, the horizontal motion and the vertical motion are independent of each other.  Neither component’s motion affects the other.

 No horizontal acceleration  Horizontal velocity is constant  Horizontal motion is linear in time

 Vertical acceleration due to gravity  Vertical velocity is linear in time  Vertical motion is quadratic in time

 A baseball is hit from a height of 0.80 m above the ground with an initial velocity of 37 m/s at an angle 29° above horizontal. a) What is the baseball’s maximum height? b) How far away does the baseball land?

 A soccer ball is kicked so that its horizontal velocity is 12.6 m/s and its vertical velocity is 10.9 m/s. What is the magnitude and direction of the ball’s velocity?

 You will have an opportunity to retake the test.  Before taking the retake, you must follow the test corrections directions on the web site. ◦ This is a LONG process. ◦ Must be turned in by 3:30 this Friday.  Retake may only be taken: ◦ Monday, October 12 at lunch ◦ Tuesday, October 13 at lunch ◦ Tuesday, October 13 after school  Retake will be more difficult that the original test.  The highest grade you can get is 85%.  If you get lower than your original grade, then you keep your original grade.

Test Answers – page 4

 No horizontal acceleration  Horizontal velocity is constant  Horizontal motion is linear in time

 Vertical acceleration due to gravity  Vertical velocity is linear in time  Vertical motion is quadratic in time

 A bullet is shot from the ground at 485 m/s at an angle 70.0° above the horizontal. How far away will it land?

 A ball rolls off of a 120 cm tall horizontal table at 7.25 cm/s. How far away from the table does the ball land?

 On the website  Some of the problems are difficult  Some of the problems are very difficult  #1-2 due Monday  #3-4 due Tuesday  #5-6 due Thursday  #7-8 due Friday  If you have time after today’s lab, work on the worksheet with your partner

 Groups of 3-4 (assigned by Mr. Szwast)  Measure and record the height of the table.  Follow procedures #1-8 (including the graph) ◦ Your graph should fill up a full page of graph paper  Answer #1-2 before attempting extra credit.  You may answer #3 after attempting extra credit. ◦ You only get one chance at the extra credit.

 A baseball is thrown from a height of 1.87 m at 27.3 m/s, 15° above horizontal, to the first baseman, 9.5 m away. Which of the following will happen? a) The ball will go over the first baseman’s head. b) The first baseman will catch the ball before the ball has a chance to hit the ground. c) The ball will hit the ground before it makes it to the first baseman.

 On the website  Some of the problems are difficult  Some of the problems are very difficult  #1-2 due Monday  #3-4 due Tuesday  #5-6 due Thursday  #7-8 due Friday  If you have time after today’s lab, work on the worksheet with your partner

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