In an experiment similar to Lab 4, a spring loaded gun launches a projectile inclined up at an angle θ to the table top. The altitude of the projectile (y, in m) above the floor is determined by having the projectile hit a (movable) wall that has been placed some horizontal distance (x, in m) from the gun. The altitude measurements have an accuracy of 0.005 m. Newton predicts that the altitude of the projectile will fit a quadratic relationship:

y = y0 + tan(θ) x - 0.5 g x2/(vx0)2

where g = 9.8 m/s2 is the acceleration of gravity and vx0 is the projectile's velocity in the x direction.

  1. Fit this data with a quadratic relationship.
  2. Consider Newton's scientific claim of an quadratic law. Does this evidence (data) confirm or contradict this claim? Support your answer quantitatively.
  3. Properly report (sigfigs, error, units) the A, B and C parameters of the best-fit relationship.
  4. Use a spreadsheet to calculate the launch angle θ -- the spreadsheet function for the inverse tangent is atan, so

    θ (in radians) = atan(B)

    Find the error in θ using the "high-low" method.

  5. Properly report (sigfigs, error, units) the value for θ.
  6. Self-document the spreadsheet and turn in a hardcopy of the page.
  7. Make a hardcopy plot of the data with best-fit curve.

X
(m)		Y
(m)
0.10.887
0.20.955
1.11.255
1.41.231
1.61.176
1.71.132
2.00.978
2.70.326
2.80.211
2.90.077