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UI PHYS 1200 - Mechanics 4

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1Review: motion with constant acceleration• a = 0 case• no acceleration  velocity is constant  v = vi• position vs. time  xf= x i+ v t, xiis the starting position• acceleration = a = constant• velocity vf= vi+ a t, viis the velocity at time t = 0• position if motion starts at xi= 0, with vi= 0 (at rest) x = ½ a t2• for problems in free-fall with vi = 0, then a = g (= 10 m/s2) vf= g t and yf= ½ g t2 1Acceleration: change in velocity / time intervalReview: Free fall- object projected vertically up• Time to reach the maximum height• Total time in the air2Position, yTime, ttup2tupVelocity, vTime, t0viviHUPDOWNiupvt = gup downiupt = t , sovt = t + t = 2gair downexampleProblem: An object is dropped from rest from a height of 20 m above the ground.(a) How long will it take to reach the ground? (b) What is its velocity as it hits the ground?Solution: initial velocity, vi= 0yf= ½ g t2, v = g t 2f22f2y 2×20 m(a) t = = = 4 s = 2 sg 10 m/s(b) v = g t = 10 m/s × 2 s = 20 m/s3L-5 Projectile motion4• A projectile is an object that is thrown,hit, kicked, shot, etc., and then travels under the influence of gravity.• It is an example of two-dimensional motion.Projectile Examples• Tennis ball• Golf ball• Football• Softball• Soccer ball• bullet• Hockey puck or ball• Basketball• Volleyball• Arrow• Shot put• JavelinThese are all examples of things that are launched, then move under the influence of gravity5Not projectiles• Jet plane• Rocket• Car (unless it looses contact with ground)• catapult (before rock leaves)• slingshot (before rock leaves sling)62Unintended projectile7 The key to understanding projectile motion is to realize that gravity acts in the vertical (downward) direction gravity affects only the vertical motion, not the horizontal motionProjectile motionforce ofgravity8Demonstration• We can show that the horizontal and vertical motions are independent• The red ball was released and falls vertically down• The yellow ball was given a kick to the right.• They track each other vertically step for step and hit the ground at the same time9Galileo’s inclined plane experimentsNO!YES!10In the absence of gravity a bullet would follow a straight line forever.With gravity it FALLS AWAY fromthat straight line!Target practice11Hitting the target – aim high, not directly at the target123Sports without gravity13Baseball14Every hit ballis a line drivePop-ups neverCome down.Basketball – no jump shots!Withgravity15WithoutgravityKicking field goals would be easier!16100 yard field goalswould be possible.Path of the Projectile: parabolavDistance down rangeHeightrisingfallinggHorizontal velocityVerticalvelocityv17projectileangle ofelevationProjectile motion – key points1) The projectile has both a vertical and horizontal component of velocity2) The only force acting on the projectile once it is released is gravity (neglecting air resistance)3) At all times the acceleration of the projectile is g = 10 m/s2downward4) The horizontal velocity of the projectile does not change throughout the path5) On the rising portion of the path gravity causes the vertical component of velocity to decease184key points-continued6) At the very top of the path the vertical component of velocity is ZERO7) On the falling portion of the path the vertical velocity increases8) When the projectile lands it will have the same vertical speed as it began with9) The time it takes to get to the top of its path is the same as the time to get from the top back to the ground10)The range of the projectile (horizontal distance travelled) depends on its initial speed and angle of elevation19Maximum Range• When an artillery shell is fired the initial speed of the projectile depends on the explosive charge which cannot be easily changed• The only control is setting the angle of elevation.• You can control the range (where it lands) by changing the angle of elevation• To get maximum range set the angle to 45°2065°45°25°15°The ultimate projectile:putting an object into orbitNEWTON• Imagine trying to throw a rock aroundthe world.• If you give it a large horizontal velocity, it will go into orbit around the


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UI PHYS 1200 - Mechanics 4

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