Parametric Equations

Parametric Equations Day 2
TS: Examining Information from more than one viewpoint
Warm Up: Eliminate the parameter and then sketch the graph. Do
not forget your directional arrows.
x  ln(2t )
y  2t
Projectile Motion Model
x  (vo cos  )t
y  h  (vo sin  )t  16t
h = initial launch height
Vo = initial velocity
θ = angle with horizontal object was initially
launched at
A ball is initially hit at a height of 7ft at an angle of 35°. If
someone 30 yards away catches the ball at a height of 4
feet, what was the initial velocity of the ball? Also how
long was the ball in flight?
Two opposing players in “Capture the Flag” are 100ft apart.
On a signal, they run to capture a flag that is on the ground
midway between them. The faster runner, however,
hesitates for 0.1 sec. The following parametric equations
model the race to the flag:
x1  10(t  0.1), y1  3
x2  100  9t , y2  3
a) Simulate the game in a [0, 100] by [-1, 10] viewing window
with a t starting at 0. Graph simultaneously.
b) Who captures the flag and by how many feet?