#### Transcript 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*

*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?