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Due Now: By the end of the day today, IWBAT… • use trigonometry and the kinematic equations to solve for angled projectiles Do Now: Calculate the magnitude of the vertical and horizontal components of the following vector: 65 m/s 32˚ Tuesday, November 6, 2012 Angled Projectiles What we know about projectiles so far… A projectile is any object upon which the only force is gravity Projectiles travel with a parabolic trajectory due to the influence of gravity There are no horizontal forces acting upon projectiles and thus no horizontal acceleration The horizontal velocity of a projectile is constant There is a vertical acceleration caused by gravity; its value is 9.8 m/s2, which means the vertical velocity of a projectile changes by 9.8 m/s each second The horizontal motion of a projectile is independent of its vertical motion Symmetrical Nature of a Projectile A ball is thrown with an initial velocity of 41.7 m/s at a 70˚ angle Position vx vy 1 14.3 m/s 39.2 m/s 2 14.3 m/s 29.4 m/s 3 14.3 m/s 19.6 m/s 4 14.3 m/s 9.8 m/s 5 14.3 m/s 0 6 14.3 m/s -9.8 m/s 7 14.3 m/s -19.6 m/s 8 14.3 m/s -29.4 m/s 9 14.3 m/s -39.2 m/s 5 4 3 2 1 6 7 8 9 Horizontal vs. Angled Horizontal Projectiles a of x will ALWAYS be 0 vi of y will ALWAYS be 0 a of y will ALWAYS be 9.8 m/s2 tx = ty you must be given 3 out of 4 variables in order to solve! Angled Projectiles a of x will ALWAYS be 0 a of y will ALWAYS be 9.8 m/s2 use trig to find vi of x and y viy = -vfy The vfy at the peak = 0 tx = ty you must be given 3 out of 4 variables in order to solve! Here’s a problem… A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the time of flight of the football. What if… A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the horizontal distance of the football. Not done yet… A football is kicked with an initial velocity of 25 m/s at an angle of 45-degrees with the horizontal. Determine the peak height of the football. A long jumper leaves the ground with an initial velocity of 12 m/s at an angle of 28-degrees above the horizontal. Determine the horizontal distance AND the peak height of the long-jumper. Li Ping Phar, the famous Chinese ski jumper, leaves the ramp with an initial velocity of 34.9 m/s at an angle of 35°. a. Determine the total time of flight. b. Determine the horizontal displacement. c. Determine the peak height (relative to the starting height). Assume that Li lands at the same height as the top of the ramp and that Li is a projectile. CHALLENEGE QUESTION! Albert is South’s star punter for the varsity football team. His best hang time this past season was for a punt which he kicked at 74° above the horizontal. The punt had a 6.2 second hang time. a. Determine the speed at which the ball was punted. b. Determine the horizontal distance which the ball traveled.