slope <- function(x,y) sum(x*y) / sum(x^2)
x <- c(1:10)
m0 <- 3; y <- m0 * x  
x
y
m0 <- 3; y <- m0 * x  + rnorm(10, 0, 0.5)  
y
plot(x,y)
plot(x,y, xlim=c(0, 10), ylim=c(0, 35) )
grid()
m <- slope(x,y)
m
abline(0,m)
t <- seq(0, 10, by=0.1) 
t
v0 <- 20 # m/s 
th <- 45 * pi/180 ;  x0x <- v0 *cos(th) ; v0y <- v0*sin(th)  
th
th <- 45 * pi/180 ;  v0x <- v0 *cos(th) ; v0y <- v0*sin(th)  
v0x
v0y
x <- v0x * t ;  y <- v0y * t + 1/2 * (-g)*t^2  
g <- 9.8 # m/s^2
x <- v0x * t ;  y <- v0y * t + 1/2 * (-g)*t^2  
plot(x,y, asp=1)
plot(x,y, asp=1, col='blue', cex=0.5)
grid()
th <- 20 * pi/180 ;  v0x <- v0 *cos(th) ; v0y <- v0*sin(th)  
x <- v0x * t ;  y <- v0y * t + 1/2 * (-g)*t^2  
points(x,y, col='blue', cex=0.5)
th <- 80 * pi/180 ;  v0x <- v0 *cos(th) ; v0y <- v0*sin(th)  
x <- v0x * t ;  y <- v0y * t + 1/2 * (-g)*t^2  
points(x,y, col='blue', cex=0.5)
max(t)
q()