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



y



2

t

2

Projectile Motion Model

x



(

v o



t y

(

v o



t



16

t

2 Where: 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:

x x

2 1  10(

t

  0.1),

y

2

y

1   3 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?