Calc10_4 - 10.4 Projectile Motion Fort Pulaski GA Photo by...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
10.4 Projectile Motion Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 Fort Pulaski, GA
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
One early use of calculus was to study projectile motion . In this section we assume ideal projectile motion: Constant force of gravity in a downward direction Flat surface No air resistance (usually)
Image of page 2
We assume that the projectile is launched from the origin at time t =0 with initial velocity v o . o v Let o o v = v ( 29 ( 29 then cos sin o o o v v α α = + v i j The initial position is: r 0 0 0 o = + = i j α
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
o v α Newton’s second law of motion: Vertical acceleration f ma = 2 2 f d r m dt =
Image of page 4
o v α Newton’s second law of motion: The force of gravity is: Force is in the downward direction f ma = f mg = - j 2 2 f d r m dt =
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
o v α Newton’s second law of motion: The force of gravity is: f ma = f mg = - j 2 2 f d r m dt = mg = - j 2 2 d r m dt
Image of page 6
o v α Newton’s second law of motion: The force of gravity is: f ma = f mg = - j 2 2 f d r m dt = mg = - j 2 2 d r m dt
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 2 d r g dt = - j Initial conditions: r r v when o o dr t o dt = = = 2 o 1 r v r 2 o gt t = - + + j 2 1 r 2 gt = - j 0 + ( 29 ( 29 cos sin o o v t v t α α + + i j o v dr gt dt = - + j
Image of page 8
( 29 ( 29 2 1 r cos sin 0 2 o o gt v t v t α α = - + + + j i j ( 29 ( 29 2 1 r cos sin 2 o o v t v t gt α α = + - i j Vector equation for ideal projectile motion:
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern