Question

a projectile motion is defined as follows: $y = -\frac{1}{2}gt^2 + v_0t + y_0$ $v_0 = 40 m/s$, t: second, y: meter, $g = 9.8 m/s^2$ \begin{tabular}{|c|c|c|c|c|} \hline t(s) & 0 & 1 & 2 & 3 & 4 \\ \hline y(m) & 0 & 35.1 & 60.4 & 75.9 & 81.6 \\ \hline \end{tabular} Calculate derivative $(\frac{dy}{dt})$ at t = 2 second a) Analytical Method b) Central difference c) Backward difference d) forward difference e) write Second order lagrange polynomial and find the $\frac{dy}{dt}$ f) write Newton 3rd order Newton Divided difference and find the $\frac{dy}{dt}$ 2. Calculate $\int_0^3 \frac{x^2 \sin(x)e^x}{1 + x^2} dx$ integral using Simpson $\frac{1}{3}$ and Simpson $\frac{3}{8}$ taking n=1, n=2?

          a projectile motion is defined as follows: $y = -\frac{1}{2}gt^2 + v_0t + y_0$
$v_0 = 40 m/s$, t: second, y: meter, $g = 9.8 m/s^2$
\begin{tabular}{|c|c|c|c|c|}
\hline
t(s) & 0 & 1 & 2 & 3 & 4 \\
\hline
y(m) & 0 & 35.1 & 60.4 & 75.9 & 81.6 \\
\hline
\end{tabular}
Calculate derivative $(\frac{dy}{dt})$ at t = 2 second
a) Analytical Method
b) Central difference
c) Backward difference
d) forward difference
e) write Second order lagrange polynomial and
find the $\frac{dy}{dt}$
f) write Newton 3rd order Newton Divided difference
and find the $\frac{dy}{dt}$
2. Calculate $\int_0^3 \frac{x^2 \sin(x)e^x}{1 + x^2} dx$ integral using
Simpson $\frac{1}{3}$ and Simpson $\frac{3}{8}$ taking n=1, n=2?

a projectile motion is defined as follows: y = -(1)/(2)gt^2 + v0t + y0
v0 = 40 m/s, t: second, y: meter, g = 9.8 m/s^2

t(s) 0 1 2 3 4

y(m) 0 35.1 60.4 75.9 81.6

Calculate derivative ((dy)/(dt)) at t = 2 second
a) Analytical Method
b) Central difference
c) Backward difference
d) forward difference
e) write Second order lagrange polynomial and
find the (dy)/(dt)
f) write Newton 3rd order Newton Divided difference
and find the (dy)/(dt)
2. Calculate ∫0^3 (x^2 sin(x)e^x)/(1 + x^2) dx integral using
Simpson (1)/(3) and Simpson (3)/(8) taking n=1, n=2?

Added by Erica H.

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