Answer to Question #157948 in Classical Mechanics for Muhamad Rais B Rahman

Question

An object of mass m and initial position ⃗r₀ and initial velocity ⃗v₀ is moving under the action of the gravitational force near to earth surface at some latitude λ. Neglect the effects of both the air resistance and wind.

a) Choose your latitude and describe your system in detail.

b) Name all the forces acting on the object and sketch the free-body diagram (FBD) due to the dominant forces only.

c) Write the equation of motion (EOM) for the object and its general solutions.

d) Use relevant octave script to plot the position (trajectory) of the object when it is released from initial height z’₀ = h₀ and describe the motion.

e) Use the same script to plot the position of the object when it is launched with initial velocity ⃗v₀ at initial position ⃗r₀ and describe the motion.

Answer 1

Given,

Mass of the object =m

Initial position= $(\overrightarrow{r_o})$

Position of latitude $=(\lambda)$

b)

c) Here gravitation force working on the particle in the vertical direction towards the center but in the horizontal direction there is no force. Hence

$\overrightarrow{v}=\overrightarrow{u}-\overrightarrow{g}t$

$\Rightarrow \overrightarrow{h}=\overrightarrow{u}t-\frac{gt^2}{2}$

d)