1. Precalculus
8-7 Modeling Motion Using Parametric Equations
**Suppose a football player kicks a football with an initial velocity of 29 yards
per 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 projectile
relative 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 an
initial velocity of 16 feet per second at an angle of 38° with the ground.

2. • 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 that
time?
b) Suppose the kick returner lets the ball hit the ground instead of catching it. What
is the hang time of the ball? (Hint: What time t is the vertical height 0?)
HW p. 531 (9 – 15, 17, 21 all)