Calculus (With Analytic Geometry)(8th edition)

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Finding the optimal angle to throw the javelin (p. 185 Calculus text) Finding the optimal angle at which to throw the javelin: 2 2 2 0 sec (tan ) , 0 2 2 g y x x h v θ π θ θ = + + Verification of this equation relating x and y : If 0 ν is the velocity at an angle of θ with the horizontal, then 0 cos ν θ is the velocity in the horizontal direction and 0 sin ν θ is the velocity in the vertical direction. The above equation will be verified in class using the following two facts (good, to a first approximation, assuming no air resistance): 1. The acceleration due to gravity is constant (and is equal to g ) and only affects the motion in the vertical direction. 2. The velocity in the horizontal direction is constant (until the javelin hits the ground). Now, setting 0 y = we find that the (positive) solution for the distance the javelin travels is given by 2 2 0 0 0 cos sin sin 2 v x v v gh g θ θ θ = - - - (*) Computing the derivative of x with respect to θ we find 2 2 2 0 2 2 0 2 0 2 cos sin sin sin 2 sin v dx gh d g v gh v θ θ θ θ θ θ - = - + - + - Since the left-most term in square brackets is positive (note that
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
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