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Given a right triangle with acute angle θ: θ
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For the given triangle, calculate sine, cosine, and tangent: 3.0 4.0 θ
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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
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A component of a vector is its projection onto an axis (x-axis or y-axis).
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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?
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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?
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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?
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A car drives 25 miles east and 60. miles north. What is the direction and magnitude of the car’s displacement?
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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
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To add vectors: add the x-components add the y-components
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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?
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In projectile motion, the horizontal motion and the vertical motion are independent of each other. Neither component’s motion affects the other.
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No horizontal acceleration Horizontal velocity is constant Horizontal motion is linear in time
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Vertical acceleration due to gravity Vertical velocity is linear in time Vertical motion is quadratic in time
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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?
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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?
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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.
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Test Answers – page 4
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No horizontal acceleration Horizontal velocity is constant Horizontal motion is linear in time
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Vertical acceleration due to gravity Vertical velocity is linear in time Vertical motion is quadratic in time
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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?
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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?
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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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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.
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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.
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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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