### Typo corrections and minor updates in the explanations

parent 865fd726
 ... ... @@ -8,20 +8,30 @@ "## Animate a bouncing ball\n", "\n", "Solve the equations of motion for the position and velocity of a ball as a function of time. \n", "Change in position $x$ and velocity $v$ over the time interval $\\Delta t$ are\n", "Changes in position $x$, $y$ and velocity $v$ over the time interval $\\Delta t$ are\n", "$$\n", "\\Delta x = v \\cdot \\Delta t \\\\\n", "\\Delta v = a \\cdot \\Delta t\n", "\\Delta x = v_x \\cdot \\Delta t \\\\\n", "\\Delta y = v_y \\cdot \\Delta t \\\\\n", "\\Delta v_y = a \\cdot \\Delta t\n", "$$\n", "\n", "With only gravitational acceleration acting we have $a = g = 9.81 \\text{m}/\\text{s}^2$\n", "Assume $v_x$ is constant and only gravitational acceleration is acting, i.e. $a = g = 9.81 \\text{m}/\\text{s}^2$. If position $y < 0$ the ball bounces with a coefficient of $coe_b = 0.7$.\n", "\n", "\n", "Let $x_1$ and $v_1$ be the initial position and velocity and $x_2$ and $v_2$ denote the position and velocity after the time interval $Δt$. We can use the above equations, and $Δx=x_2−x_1$, $Δv=v_2−v_1$, to solve for $x_2$ and $v_2$.\n", "Let $x_1$, $y_1$ and $v_{x1}$, $v_{y1}$ be the initial position and velocity and $x_2$, $y_2$ and $v_{x2}$, $v_{y2}$ denote the position and velocity after the time interval $Δt$. With the above equations and $Δx=x_2−x_1$, $Δy=y_2−y_1$, $Δv=v_2−v_1$, $v_x = constant$, solve for $x_2$, $y_2$ and $v_2$ (dropping the index $y$ from now on, i.e. $v_y = v$, as $v_x = v_{x0}$ = const).\n", "$$\n", "x_2=x_1+v_1Δt \\\\\n", "x_2=x_1+v_{x0}Δt \\\\\n", "y_2=y_1+v_1Δt \\\\\n", "v_2=v_1+aΔt\n", "$$ " "$$\n", "if y < 0 the ball bounces: \n", "$$\n", "y_i = 0\\\\\n", "v_i = -v_{i-1} * coe_b\n", "\n", "\n", "\n", " *Note:* Be patient as the animation takes a few seconds to display!" ] }, {
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