Precalculus8-7 Modeling Motion Using Parametric Equations **Suppose a football player kicks a football with an initial velocity of 29 yardsper second at an angle of 68°. Suppose a kick returner catches the ball 5 seconds later.How far has the ball traveled horizontally and what is its vertical height at that time?Objects that are launched (like a football) are called _____________________________.The ______________ of a projectile is called its ____________________________.The horizontal distance that a projectile travels is its _______________________.The motion of a projectile can be described by its position, _______________________,and acceleration. • These can all be represented by ______________________.Parametric equations can represent the _____________________ of the projectilerelative to the starting point in terms of the parameter of ____________. • To find the parametric equations, we must write the ___________________ and ____________________ components of the initial velocity.EX1: Find the initial horizontal velocity and vertical velocity of a stone kicked with aninitial velocity of 16 feet per second at an angle of 38° with the ground.
• Because gravity does not affect horizontal velocity, it is the _______________________ of the horizontal component of the initial velocity.Therefore, the horizontal position of a projectile after t seconds is: • Since vertical velocity is affected by gravity, we must __________________ the vertical component of initial velocity. • We can determine the _____________ of the projectile after t seconds by subtracting _______________________ effect from the initial velocity.EX2: Refer to ** at the beginning of the notes.a) How far has the ball traveled horizontally and what is its vertical height at thattime?b) Suppose the kick returner lets the ball hit the ground instead of catching it. Whatis the hang time of the ball? (Hint: What time t is the vertical height 0?)HW p. 531 (9 – 15, 17, 21 all)