Projectile Motion PDF

Projectile Motion  Motion of a Projectile Have you noticed how a basketball player makes a three-point score? https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Three_point_shoot.JPG/1200px- Three_point_shoot.JPG  An object t...

Projectile Motion  Motion of a Projectile Have you noticed how a basketball player makes a three-point score? https://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Three_point_shoot.JPG/1200px- Three_point_shoot.JPG  An object thrown with an initial horizontal velocity and acted upon by the earth’s pull of gravity is known as a projectile. A projectile travels in a curved path called the trajectory. https://images. slideplayer.com /31/9782965/sli des/slide_3.jpg https://www.quintic.com/education/imagesforeducation/PM1.jpg  https://volleyball- tips.com/wp- content/uploads/2 019/01/jump- serve-photo- e1546897100292. jpg https://blog.playo.co/wp-content/uploads/2017/06/free- throw-shoot3.jpg https://cdn.theatlantic.com/thumbor/BVHuJyVB5GLexptClHahRNaSFqE=/900x580/media/img/phot https://www.futurity.org/wp/wp-content/uploads/2020/08/baseball-vision-training-batting_1600.jpg o/2013/11/the-philippines-one-week-after-typhoon-haiyan/h22_87969396/original.jpg https://useruploads.socratic.org/UB8GyFkoSmKA1tkflfyA_vectors-projectile- motion-20-728.jpg  HORIZONTAL PROJECTIONS The velocity of a projectile can be separated into horizontal and vertical components. The vertical component (vy) varies while the horizontal component (vx) is constant. https://miro.medium.com/max/852/1*ZhGD7G6vzQQroi6Y56hFZw.png  vx vR vy vR2= vx2 + vy2 vR = 𝑣𝑥2 + 𝑣𝑦2 The maximum height (dy) and the horizontal distance (dx) can be calculated by using the formula for a freely falling body and that for constant speed motion. 𝑔𝑡2 dy = 2 and dx = vx. t Sample Problems. 1. A little girl throws her jackstone ball horizontally out of the window with a velocity of 3.0m/s. If the window is 3.0 m above the level ground, how far will the ball travel before it hits the ground?  2. Paul is standing outside the Physics laboratory 7.0m from the wall. Peter, by a window 5.0 m above the ground, tosses the ball horizontally. Find the speed that Peter should give the ball for it to reach Paul.  Projections at Arbitrary Angles When a projectile is fired with an initial velocity (vi) at an angle θ above the horizontal, the initial velocity can be resolved into its rectangular components. That is, vix = vi cos θ viy = vi sin θ  2 dy = 𝑣𝑖𝑡 + 𝑔𝑡 2 2 2 𝑣𝑓𝑦 −𝑣𝑖𝑦 dy = 2𝑔 Hence, vfy = viy + gt  As the projectile rises, it decreases its vertical velocity and, at the peak of the trajectory, it becomes zero. Thus, the time for a projectile to rise can be resolved by the equation, vfy = viy – gt where vfy = 0 0 = viy – gt 𝑣𝑖𝑦 𝒗𝒊 𝐬𝐢𝐧 𝜽 t= t= 𝑔 𝒈  To find the total time (t’) of flight that a projectile is in the air, simply double the time it takes a projectile to rise. 𝒗𝒊 𝐬𝐢𝐧 𝜽 t= 𝒈 2t  The maximum height (dy) can be calculated by considering the downward motion of a projectile, wherein viy = 0 (from the peak).  The horizontal displacement known as the range (R or dx) of the projectile is the product of the horizontal velocity and the total time of flight. SAMPLE PROBLEM.  A long jumper leaves the ground at an angle of 30 0 to the horizontal and at a speed of 6.0 m/s. How far does he jump?