- #1
uchicago2012
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Homework Statement
Suppose we attempt to account for air resistance in our projectile motion in the following (incorrect) way: we alter g so that the acceleration in the y direction is -8 m/s2, and introduce a horizontal acceleration of -3 m/s2. With these changes, find the landing point of a projectile fired with initial speed 32 m/s at an angle of 25°.
Homework Equations
x - x0 = (v0 cos theta0)t + 1/2 at2 (note this is changed from the textbook definition- by the addition of the term (+ 1/2 at2)- bc of the introduction of horizontal acceleration)
y - y0 = (v0 sin theta0)t + 1/2 at2
vy = v0 sin theta0 + at
vy2 = (v0 sin theta0)2 + 2a(y - y0)
and other constant acceleration equations altered for the purposes of projectile motion
for constant acceleration:
R = (2v02/g) (sin 2theta0)
where R = the horizontal range of the projectile
The Attempt at a Solution
I was wondering if there was a way to solve this without assuming the landing point is the same as the launch point (constant elevation.) I solved it assuming constant elevation, but as it doesn't say that, I don't know if that was perhaps a bad assumption.
With my assumption, I found that the projectile's landing point was 80.9 m from its starting point.