2. Physics 121

3. 3. Kinematics in 2-D and Vectors 3.1 Vectors and Scalars 3.2 Addition of Vectors - Graphically 3.3 Subtraction and Scalar Multiplication 3.4 Addition of Vectors - Analytically 3.5 Projectile Motion 3.6 Projectile Motion Problems 3.7 Projectile Motion is Parabolic 3.8 Relative Velocity

4. Example 3.1... Can 3 + 4 = 5? Give examples of Scalar and Vector quantities You drive 3 miles East and then 4 miles North. How far are you from your starting point? 5 miles What is the difference between distance and displacement? Distance is a Scalar (has magnitude only) and displacement is a Vector (direction is also required). Scalars: speed and density Vectors: velocity and force

5. Trig Review Pythagorean Theorem: a 2 + b 2 = c 2 sin  = opposite / hypotenuse = a /c cos  = adjacent / hypotenuse = b / c tan  = opposite / adjacent = a / b  c b a

6. Example 3.2... Vector Addition You drive 3 miles East and then 4 miles Northeast. What is your net displacement (magnitude and direction)? Solve it (a) graphically (b) analytically

7. Solution 3.2(a)... Graphical Vector Addition 3 4 45 0 ? ? E N

8. Solution 3.2(a)... Graphical Vector Addition 3 4 45 0 6. 4 26 0 E N Resultant displacement vector is 6.4 m, 26 0 North of East

9. Solution 3.2(b)... Analytical Vector Addition Vector X = V cos  Y = V sin  3 at 0 0 3 0 4 at 45 0 2.8 2.8 Resultant 5.8 2.8 R 2 = X 2 + Y 2 R 2 = (5.8) 2 + (2.8) 2 R = 6.4 tan  = Y / X tan  = 2.8 / 5.8  = 26 0

10. A picture is worth 10 3 words !!! 3 4 2.8 3 5.8 2.8 6.4

11. Projectile Motion 1.Which projectile reaches the ground first? 2.Which is moving faster just before impact? Two objects are launched horizontally with different speeds

12. Projectile Motion 1.Same Time 2.Different Speeds Two objects are launched horizontally with different speeds

13. Example 3.3... Projectile Motion Given h= 20 m and V H = 7 m/s. Calculate (a) Time to hit the ground (b) Range D (c) Impact Speed h D

14. Solution 3.3... Projectile Motion V 2 = (20) 2 + (7) 2 V = 21.2 m/s h = ½ a t 2 t = 2 s D = (7 m/s)(2 s) D = 14 m V v = 0 + at V v = 0 + (10)(2) V v = 20 m/s

15. Example 3.4... Soccer Ball A soccer ball is kicked and it is projected with a speed of 20 m/s at an angle of 30 0. How far away does it land? D

16. Solution 3.4... Soccer Ball D = (V H )(t) D = (20 cos 30 0 )(2) D = 34.6 m V v = 20 sin 30 0 = 10 m/s So air time is 1s (up) and 1s(down) = 2 s

17. That’s all folks!