Given these assumptions, the following steps are then used to analyze projectile motion:

Step 1.Resolve or break the motion into horizontal and vertical components along the x- and y-axes. These axes are perpendicular, so
${A}_{x}=A\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta $ and
${A}_{y}=A\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\theta $ are used. The magnitude of the components of displacement
$\mathbf{s}$ along these axes are
$x$ and
$\mathrm{y.}$ The magnitudes of the components of the velocity
$\mathbf{v}$ are
${v}_{x}=v\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\theta $ and
${v}_{y}=v\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\mathrm{\theta ,}$ where
$v$ is the magnitude of the velocity and
$\theta $ is its direction, as shown in
[link] . Initial values are denoted with a subscript 0, as usual.

Step 2.Treat the motion as two independent one-dimensional motions, one horizontal and the other vertical. The kinematic equations for horizontal and vertical motion take the following forms:

$\text{Horizontal Motion}({a}_{x}=0)$

$x={x}_{0}+{v}_{x}t$

${v}_{x}={v}_{0x}={v}_{x}=\text{velocity is a constant.}$

$\text{Vertical Motion}(\text{assuming positive is up}\phantom{\rule{0.25em}{0ex}}{a}_{y}=-g=-9.\text{80}{\text{m/s}}^{2})$

Step 3.Solve for the unknowns in the two separate motions—one horizontal and one vertical. Note that the only common variable between the motions is time
$t$ . The problem solving procedures here are the same as for one-dimensional
kinematics and are illustrated in the solved examples below.

Step 4.Recombine the two motions to find the total displacement$\mathbf{\text{s}}$and velocity$\mathbf{\text{v}}$ . Because the
x - and
y -motions are perpendicular, we determine these vectors by using the techniques outlined in the
Vector Addition and Subtraction: Analytical Methods and employing
$A=\sqrt{{A}_{x}^{2}+{A}_{y}^{2}}$ and
$\theta ={\text{tan}}^{-1}({A}_{y}/{A}_{x})$ in the following form, where
$\theta $ is the direction of the displacement
$\mathbf{s}$ and
${\theta}_{v}$ is the direction of the velocity
$\mathbf{v}$ :

During a fireworks display, a shell is shot into the air with an initial speed of 70.0 m/s at an angle of
$\mathrm{75.0\xba}$ above the horizontal, as illustrated in
[link] . The fuse is timed to ignite the shell just as it reaches its highest point above the ground. (a) Calculate the height at which the shell explodes. (b) How much time passed between the launch of the shell and the explosion? (c) What is the horizontal displacement of the shell when it explodes?

Strategy

Because air resistance is negligible for the unexploded shell, the analysis method outlined above can be used. The motion can be broken into horizontal and vertical motions in which
${a}_{x}=0$ and
${a}_{y}=\u2013g$ . We can then define
${x}_{0}$ and
${y}_{0}$ to be zero and solve for the desired quantities.

Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest.
Rafiq

Rafiq

what is differents between GO and RGO?

Mahi

what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.?
How this robot is carried to required site of body cell.?
what will be the carrier material and how can be detected that correct delivery of drug is done
Rafiq

Rafiq

if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION

Anam

analytical skills graphene is prepared to kill any type viruses .

The nanotechnology is as new science, to scale nanometric

brayan

nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale

Damian

Is there any normative that regulates the use of silver nanoparticles?