1 / 4

Trigonometric Model: Soccer Ball Distance Equation

Derive the horizontal distance equation for a soccer ball kicked from ground level at a given speed and angle. Learn the reasoning behind maximizing the distance travel.

pforrest
Download Presentation

Trigonometric Model: Soccer Ball Distance Equation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Soccer Write an equation for the horizontal distance traveled by a soccer ball kicked from ground level (h0 = 0) at speed vand angle q. EXAMPLE 4 Derive a trigonometric model

  2. 16 – = 0 x2 + (tanq )x + 0 v 2 cos2q 1 16 16 = 0 – x( x – tanq ) v 2 cos2q 16 = 0 x – tanq v 2 cos2q 16 = tanq x v 2 cos2q Multiply each side by 1 x v2 cos2q. 16 = v2 cos2q tan q EXAMPLE 4 Derive a trigonometric model SOLUTION Leth0 = 0. Factor. Zero product property Add tan q to each side.

  3. = x v2 cos qsinq 1 1 1 1 1 x = v2(2cos qsinq) Rewrite as 2. 16 32 16 32 32 x = v2sin 2q EXAMPLE 4 Derive a trigonometric model Use cos q tan q= sin q. Use a double-angle formula.

  4. REASONING: Use the equation x = v2sin 2 q to explain why the projection angle that maximizes the distance a soccer ball travels is q = 45°. 10. 1 32 ANSWER ANSWER No sin 2(45°) = sin 90° = 1, this is the only value that will not decrease the velocity of the ball since it is the only non-fractional value. for Examples 4 GUIDED PRACTICE 9. WHAT IF? Suppose you kick a soccer ball from ground level with an initial speed of 70 feet per second. Can you make the ball travel 200 feet?

More Related