Physics 121

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

Example Can = 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

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

Example 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

Solution 3.2(a)... Graphical Vector Addition ? ? E N

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

Solution 3.2(b)... Analytical Vector Addition Vector X = V cos  Y = V sin  3 at at Resultant 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

A picture is worth 10 3 words !!!

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

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

Example 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

Solution 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

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

Solution 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

That’s all folks!