Parametric Equations Day 2TS: Examining Information from more than one viewpoint

Warm Up: Eliminate the parameter and then sketch the graph. Do not forget your directional arrows.

2

ln(2 )

2

x t

y t

Projectile Motion Model

Where:

h = initial launch height

Vo = initial velocity

θ = angle with horizontal object was initially launched at

2

( cos )

( sin ) 16

o

o

x v t

y h v t t

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:

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?

1 1

2 2

10( 0.1), 3

100 9 , 3

x t y

x t y