LEARNING TIP Using Scientic Calculators [d] a}? = 2s m [as N of E] or = 4.9. s A warning about using scientific .. calculators: when rst turned V8\" = on. these calculators usually ' A3 express angles in degrees Vac = E [DEG]. Pushing the appropriate key (9.9., one) will change the = m units to radians [RAD] or grads M s (GHA, where 90 = 100 grads]. I!\" = 6.6 We [14" N of E] Only degrees will be used in this text The average velocity is 6.5 mfs [14 N of E]. Understanding Concepts Answers 18. Determine the vector Slim of the displacements A3, = 2.4 m [32 8 of W]; is 5.6 m [240 E Of S] Adz = 1.6 m [S]; and Ad3 = 4.9 \"1 [27 S of E]. 20. [a] 1.3 x m3 m [42 N of E] 19. Solve Sample Problem 5 using (a) a vector scale diagram [b] components (referring. if necessary, to Appendix A] 20. A skater on Ottawa's Rideau Canal travels in a straight line 8.5 X 102 m [25 N of E] and then 5.6 X to2 m in a straight line [21 Eof N].The entire motion takes o_2 min. (a) What is the skater's displacement? [b] What are the skater's average speed and average velocity? (b) 5.6 m/s; 5.2 W5 [42" N of E] LEARNING TIP Mding Vedors In applying the veEtor addition :'luayfg': E; [3:15; 33:12 SUMMARY Speed and Velocity in One motion. you can choose to add and TWO DiMEIISiOllS the displacement vectors by whichever of the methods sum- marized in AppendixA proves . , _ ' . most convenient. The vector I Average speed is the total distance travelled divided by the total time of travel. scale \"head-to-tail\" diagram I A vector quantity has both magnitude and direction. method is excel lent for visual- , , , , . , . . izing and understanding the sit- I Position is the distance With a direction from some reference pornt. uation. However. this method is I Displacement is the change of position. not as accurate as other methods. The component tech- nique is accurate and can be I Average velocity is change of position divided by the time interval for that used for any number of vectors, Changg but it can be time-consuming. The method using the sine and cosine laws is accurate and I Instantaneous speed is the magnitude of the instantaneous velocity. fairly quick to use, but it is lim- ited to the addition [or subtrac- tion) of only two vectors. I The area under the line on a velocity-time graph indicates the change of position. I A scalar quantity has magnitude but no direction. I Velocity is the rate of change of position. I Instantaneous velocity is the velocity at a particular instant. I The slope of the line on a position-time graph indicates the velocity. I In two-dimensional motion, the average velocity is the total displacement divided by the time interval for that displacement. 16 Chapter] NEL Kinematics Uniform motion (1) Accelerating (2)(3) Missing Variable Equation V = Ad At Ad = v, Al- - as/2 V 2 Ad = VAr+1ON Ad = Vi + V2 A Ad V2 = Vi + aAt At V2 = V, + 2add ** you must define a positive direction first *** Review 1: Kinematics Problems One Calculation: 1. A locomotive slows from 26.0 m/s to 0.00 m/s in 18.0 s. How far does it travel? 2. A car driving at a speed of 60.0 m/s accelerates to a speed of 85.0 m/s in 12.0 s. How far does it travel during the 12 seconds? 3. When struck by a club, a golf ball initially at rest acquires a speed of 31.0 m/s. If the bal is in contact with the club for 1.17 ms, what is the magnitude of the average acceleration of the ball? 4. The initial velocity of an electron is -2.0 x 10' m/s. If its acceleration is 4.2 x 10"* m/s? a) How far does it travel before momentarily coming to rest? b) How long will it take to undergo a displacement of 5.0 cm? 5. The Demon Drop ride at Cedar Point, Ohio, starts from rest and free falls for 1.5 s. a) How far does it fall? b) How fast is it going at the end of the 1.5 seconds? 6. An airplane travels 1800 km at a speed of 1000 km/h. It then encounters a headwind that slows it to 850 km/h for the next 2300 km. What was the average speed of the plane for this trip? 7. A stone is thrown upward from the edge of a cliff 18.0 m high. It just misses the cliff on the way back down and hits the ground below with a speed of 18.8 m/s. a) With what velocity was it released? b) What is its maximum distance from the ground during the flight?Projectile Motion Worksheet (Case 1) Name: Mod: Date: Directions: Answer the following questions below using the projectile motion equations. List all variables and show your work. Circle your final answer with the correct units. 1. An arrow is red directly horizontal off a cliff that is 10.0 meters tall with a velocity of 65.5m/s. a. How long is the arrow in the air? b. What is the range of the arrow? 2. A pool ball leaves a 0.60meter high table with an initial horizontal velocity of 2.4 m/s. a. Predict the time required for the pool ball to fall to the ground. b. Predict the horizontal distance between the table's edge and the ball's landing 3. A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of 35.0 meters from the edge of the hill. Determine the initial horizontal velocity ofthe soccer ball. 4. A rock is thrown with a velocity of 23.7m/s horizontally off the top of an elevated hill. If the time it takes to reach the ground is 5.70 seconds. What is the height of the hill? 6. You're a criminal investigator and need evidence to discover the mystery of a crash. A car traveled a horizontal distance of 22.3m before smashing into the ground after it ran off a horizontal road. The cliff is 7.2m high from the base to the top. At what speed was the car traveling at before it ran off the road? 7. A bullet is fired from a gun with an unknown velocity towards an unwary deer in the valley. If the hunter is standing on top of a hill and fires the gun horizontally at the deer which is 200 yardaway at an angle of 5.0 degrees below the horizontal. What is the initial velocity of the bullet