The image contains a chart designed to illustrate how various factors affect the path of a projectile. The factors considered are increasing launch height, increasing mass, increasing initial speed for both horizontally and non-horizontally launched projectiles, and increasing launch angles from 0-45° and 45-90°. The chart outlines how these factors influence the following variables:- Final Horizontal Velocity- Final Vertical Velocity- Time in the Air- Range- Maximum HeightThe chart is currently empty and requires completion based on knowledge or experimentation regarding projectile motion.Below the chart, there is a question:"For a non-horizontally launched projectile, how does the time it takes the projectile to rise from its launch height to its maximum height compare to the time it takes the projectile to return to its launch height?"This question prompts a discussion or calculation regarding the symmetry of projectile motion in the vertical direction.

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Description: The image contains a chart designed to illustrate how various factors affect the path of a projectile. The factors considered are increasing launch height, increasing mass, increasing initial speed for both horizontally and non-horizontally launched

Answered: Use the chart to help you describe how…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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The image contains a chart designed to illustrate how various factors affect the path of a projectile. The factors considered are increasing launch height, increasing mass, increasing initial speed for both horizontally and non-horizontally launched projectiles, and increasing launch angles from 0-45° and 45-90°. The chart outlines how these factors influence the following variables:

- Final Horizontal Velocity
- Final Vertical Velocity
- Time in the Air
- Range
- Maximum Height

The chart is currently empty and requires completion based on knowledge or experimentation regarding projectile motion.

Below the chart, there is a question:

"For a non-horizontally launched projectile, how does the time it takes the projectile to rise from its launch height to its maximum height compare to the time it takes the projectile to return to its launch height?"

This question prompts a discussion or calculation regarding the symmetry of projectile motion in the vertical direction.

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$P r o j e c t i l e m o t i o n : T h i s m o t i o n c a n b e d i v i d e d i n t o t w o d i m e n s i o n s x = u \cos θ t . . . . (1) y = u \sin θ t - \frac{g}{2} t^{2} . . . . (2) h e r e x a n d y a r e c o o r d i n a t e s o f t h e p r o j e c t i l e a t a n y t i m e i n s \tan c e t, c o n s i d e r i n g t h e p r o j e c t i l e i s l a u n c h e d f r o m o r i g i n . g i s a c c e l e r a t i o n d u e t o g r a v i t y, u i s i n i t i a l v e l o c i t y, θ i s a n g l e o f p r o j e c t i o n w i t h r e s p e c t t o h o r i z o n t a l . T h e a b o v e e q u a t i o n s a r e v a l i d w h e n, 1 . A i r r e s i s \tan c e i s i g n o r e d . 2 . M a x i m u m h e i g h t o f t h e p r o j e c t i l e i s m u c h l e s s e r t h a n r a d i u s o f t h e e a r t h . T h e e q u a t i o n f o r m a x i m u m h e i g h t i s, H = \frac{u^{2} {(\sin θ)}^{2}}{2 g} . . . . (3) R a n g e o f p r o j e c t i l e i s, R = \frac{u^{2} \sin (2 θ)}{g} . . . . (4) t i m e o f f l i g h t, T = \frac{2 u \sin θ}{g} . . . . (5) A l s o n o t e t h e t f r o m e q u a t i o n (1), t h e r e i s n o a c c e l e r a t i o n i n v o l v e d i n x - d i r e c t i o n, t h e r e f o r e, h o r i z o n t a l v e l o c i t y n e v e r c h a n g e s D i f f e r e n t i a t i n g (1) w i t h r e s p e c t t o t w e g e t v_{x} = u \sin θ . . . . (6) t h i s i s i n s \tan \tan e o u s v e l o c i t y i n x - d i r e c t i o n s i m i l a r l y d i f f e r e n t i a t i n (2) w r t t v_{y} = u \sin θ - g t . . . . (7)$

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