This Week. Next Week

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1 This Week Tutorial and Test 1, in the lab (chapters 1 and 2) Next Week Experiment 1: Measurement of Lenth and Mass WileyPLUS Assinment 1 now available Due Monday, October 5 at 11:00 pm Chapters 2 & 3 28 Projectile Motion (y-axis pointin upward, x-axis is horizontal) For projectile motion in absence of air resistance: a x = 0, a y = - 29

2 Projectile Motion Rane, Maximum eiht v y = 0 y 0 v x = v 0x = v 0 cos! v y = v 0y + a y t = v 0 sin! t In a time t, the projectile travels a distance R (rane) to the riht R = v x t t = R/v x and v x is constant In the same time, the projectile falls back to the round, at y = y 0 y y 0 = v 0y t 1 2 t2 0 = v 0y t 1 2 t2 t = 2v 0y / t = R v x = 2v 0y R = 2v xv 0y 30 Rane of a projectile R = 2v xv 0y R = v2 0 sin 2θ = 2v2 0 sin θ cos θ [2sin!cos! = sin2!] Maximum rane when! = 45 Projectile reaches maximum heiht,, when v y = 0 v 2 y = v 2 0y 2(y y 0 ) so, 0 =(v 0 sin!) 2 2 Therefore = (v 0 sin!) 2 2 e v 0 = 100 m/s,! = 30 R = 884 m, = 128 m 31

3 Projectile Motion Rane, Maximum eiht v y = 0 The projectile travels the horizontal distance R in the same time that is travels up to heiht and back down to the initial heiht. R = v2 0 sin2θ, reatest rane when θ = 45 = (v 0 sinθ) 2 2 Clickers! Balls 1 and 2 are launched from the same spot at different anles to the round. They both reach the same maximum heiht,, but ball 2 has the reater rane. 32 Decide which ball, if either, has the reater initial speed. A) Ball 1 is faster, B) Ball 2 is faster As they reach the same maximum heiht, they must have the same initial speed in upward direction, v oy1 = v oy2, so v 1 sinθ 1 = v 2 sinθ 2 33

4 Clicker Question: Focus on Concepts, Question 8: Two objects are fired into the air. The drawin shows that they reach the same heiht, but the ranes of their projectile motions are different. Which one is in the air for the reater amount of time? A) Both projectiles are in the air for the same amount of time. B) Projectile 1, because it has the smaller initial speed and, therefore, travels more slowly than projectile 2. C) Projectile 2, because it has the reater rane. D) Projectile 1, because it has the smaller rane and, hence, the horizontal component of its velocity is smaller than that of projectile Clicker Question: Focus on Concepts, Question 9 Two objects are fired into the air, and the drawin shows the projectile motions. Projectile 1 reaches the reater heiht, but projectile 2 has the reater rane. Which one is in the air for the reater amount of time? A) Projectile 1, because it travels hiher than projectile 2 B) Projectile 2, because it has the reater rane. C) Projectile 2, because it has the smaller initial speed and, therefore, travels more slowly than projectile 1. D) Both projectiles spend the same amount of time in the air. 35

5 A leopard sprins upward at a 45 0 anle and then falls back to the round. Does the leopard, at any point on its trajectory, ever have a speed that is one-half of its initial value? B A At any point: v = v 2 x + v 2 y, and v x = v 0 cos45 = v 0 / 2 At B: v y = 0, so v = v x = v 0 /!2 " 0.7v 0, which is the smallest v! The speed never falls to half its initial value. 36 Projectile Motion A y o = 1050 m v x is constant in absence of air resistance v y increases in manitude as object falls Projectile falls 1050 m in same time it travels D sideways D B y = 0 37

6 3.75/37: An airplane is flyin with a velocity of 240 m/s at an anle of 30 0 below the horizontal. When the altitude of the place is 2.4 km, a flare is released from the plane. The flare hits the taret on the round. What is the anle #? tanθ = 2.4 km, What is D? D D = v x t = v 0 t cos30. What is t? y y 0 = v 0y t 1 2 t = v 0 t sin t2 4.9t t 2400 = 0 t = s D = v 0 t cos30 = cos30 = 2712 m tanθ = θ = 41.5 D /46: A rifle is aimed at a small can. At the instant the rifle is fired, the can is released. Show that the bullet will always hit the can, reardless of the initial speed of the bullet. Bullet: Can: y b = v 0y t 1 2 t2 y c = 1 2 t2 Bullet and can meet when y b = y c : v 0y t 1 2 t2 = 1 2 t2 t = v 0y tan! = D D a y = Bullet: x = v x t = v 0 cos θ v 0 sin θ = x = D y = y = 0 tan θ That is, bullet and can are at the same place at the same time. 39

7 Relative Velocity v PT = velocity of passener relative to train v TG = velocity of train relative to round v PG =v PT +v TG v PG = velocity of passener relative to round 40 Relative Velocity If: A moves at velocityv A (relative to the round) and: B moves at velocityv B (relative to the round) then, the velocity of B relative to A is: v BA =v B v A This is the velocity of B as seen by A. 41

8 3.57/51: Two trains are passin each other. Train A is movin east at 13 m/s, train B is travellin west at 28 m/s. a) What is the velocity of train A relative to train B? b) What is the velocity of train B relative to train A? B sees A travellin to E at 41 m/s relative to it 42 Clicker Question: Focus on Concepts, Question 12 A slower movin car is travellin behind a faster movin bus. The velocities of the two vehicles are: v CG = velocity of the Car relative to the Ground = +12 m/s v BG = velocity of the Bus relative to the Ground = +16 m/s What is the velocity v BC of the Bus relative to the Car? In other words, what is the velocity of the bus as measured by the driver of the car? A) v BC = +16 m/s + 12 m/s = +28 m/s B) v BC = +16 m/s - 12 m/s = +4 m/s C) v BC = +16 m/s D) v BC = +12 m/s 43