physics

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I need some help getting a formula. I remember in class u get this really wierd looking equation like

Vicosg-((vsin(pheta))/2g)
I think this is what the equatin is when I'm asked to

"Derive a formula for the Range of a projectile based on Vi and the Launch angle, pheta. State when and why is this equation at a maximum."

I'm not exactly sure what it means by maximum or how to derrive the forumula. I think what I wrote above is what i am suppose to eventually get I'm just nore sure how to get that and what it means by maximum

  • physics -

    horizontal problem:
    u = Vi cos Theta
    range = u * time in air
    find the time in air with vertical solution:
    Vi sin theta = initial speed up
    -g = acceleration
    so
    v = Vi sin Theta - g t
    h = height = Vi sin Theta * t - .5 g t^2
    the height is zero when t = 0 and again when it hits ground at the end of flight
    0 = t (Vi sin Theta - .5 g t)
    so t = time in air = 2Vi sin Theta /g
    so
    range = Vi cos Theta * (2/g) Vi sin theta
    NOW
    if you want to know the angle Theta for maximum range
    d range/ d Theta = 0 at maximum
    0 = Vi cos Theta*(2/g)Vi cos Theta -(2/g) Vi sin theta * Vi sin Theta
    or
    cos^2 Theta = sin^2 Theta
    sin Theta/cos Theta = tan Theta = 1
    Theta = 45 degrees

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