# projectile 
times = c(0, 0.0244, 0.0489, 0.0734, 0.0979, 
          0.1226, 0.1472, 0.1719, 0.1966, 0.2214, 
          0.2462, 0.271, 0.2959, 0.3208, 0.3457,
          0.3707, 0.3957, 0.4207, 0.4459)
heights = c(0, 0.0667, 0.1207, 0.168, 0.2088, 
            0.2365, 0.2624, 0.282, 0.2955, 0.3029, 
            0.3044, 0.2977, 0.2874, 0.27, 0.2451, 
            0.2198, 0.1857, 0.1413, 0.0875)
proj = data.frame(times, heights)
# 
# plot data
plot(proj$time, proj$heights,
     main="Projectile Data",
     xlab="time (s)",
     ylab="height (m)")
#
# make a "quadratic" model
proj_fit_1 = lm(proj$heights ~ proj$times +
                  I(proj$times^2))
summary(proj_fit_1)
#
# isolating the parameters 
y0 = proj_fit_1$coefficients["(Intercept)"]
v0 = proj_fit_1$coefficients["proj$times"]
a = 2*proj_fit_1$coefficients["I(proj$times^2)"]
y0
v0
a