Introduction:
The projectile is an object on which the single force acting is gravity. There are a variety of examples of projectiles. The object dropped from rest is the projectile (given that influence of air resistance is minor). The object which is thrown vertically upward is also projectile (given that influence of air resistance is negligible). And the object that is thrown upward at the angle to horizontal is also a projectile (given that influence of air resistance is negligible). The projectile is any object which once projected or dropped goes on in motion by its own inertia and is influenced only by downward force of gravity.
Trajectory:
We can evaluate trajectory of the ball undergoing projectiles motion by plotting height y versus its x-position. We know both x and y as functions of time, and we can eliminate time dependence by using suitable equations of motion. Thus from
x = 0 + (v0cos Θ0)t+1/2(0)t2
x = v0cos Θ0t
Therefore t = x/( v0cos Θ0)
Now using the equation for y
Y = 0 + (v0sin Θ0)t - 1/2 gt2 = (v0sin Θ0)t - 1/2 gt2
Y becomes after substituting for t
Y = 0 + ((v0sin Θ0) x/(v0cos Θ0) - 1/2g(x/((v0cosΘ0)2
i.e.
y = (tan Θ0)x(-g/(2v02 cos2 Θ0)x2
We see that coefficient of x and x2 are both constants, so this equation have the form:
y = c1x - c2 x2
This is a general equation of the parabola. Therefore we conclude that trajectory of all objects moving with the constant acceleration is parabolic. So, plotting different values of x, with the corresponding values of y will trace trajectory of the projectile.
The Flight Time:
At the top of trajectory y-velocity of the projectile will be 0.0 m/s. Object is still moving at this moment, but the velocity is entirely horizontal. At the top, for the time, it has stop moving up and is set to start moving down. At that moment projectile is not moving up nor down, only across.
At the top:
Two dimensional velocity: Non-zero, aimed to right
X-velocity: Positive non-zero, equal to two dimensional velocity
Y-velocity: 0.0 m/s
At this point its motion is horizontal; i.e. the vertical component of velocity is zero. This occurs at time t = T/2. Now, we can find T/2 by putting Vy = 0 in the following Eqn.
Vy = v0sin Θ0 -gt
becomes,
0 = v0sin Θ0 -gt
So far t= T/2
0 = v0sin Θ0 -gT/2
Therefore T = (2v0/g)(sin Θ0)
Range:
If you shoot the projectile at the angle, when we compute projectile motion, set aside horizontal and vertical components of motion. This is due to force of gravity only applies on projectile in vertical direction, and horizontal component of trajectory's velocity remains uniform.
Imagine that we fire the cannonball at the angle. Given initial speed of cannonball and angle at which it was shot. To determine how far it will travel break the initial velocity into x and y components:
Vxi = Vi cos Θ
Vyi = Vi sin Θ
The given velocity components are independent and gravity applies only in y direction, which signifies that vx is constant; only vy changes with time, utilizing the given equation:
Vy = Vyi + at, or
Vy = Vi sin Θ - gt
If you want to know the x and y positions of cannonball at any time, you can easily estimate them. You know that x is:
X = Vxt=( Vi cosΘ) t
And as gravity accelerates cannonball vertically, here's what y appears (t2 here is what provides cannonball's trajectory in its parabolic shape):
Y = Vyi t-1/2gt2
You solve time it takes a cannonball to hit ground when shot straight up (ignoring air resistance) like:
Vf = Vi + at
0 = Vi - gt (at maximum height, Vf =0; a = -g = -9.8m/s2)
ttop = Vi/g
tbottom = 2Vy/g
Knowing time permits you to determine range of cannon in x direction:
S = Vxtbottom = 2VxVy/g = 2Vi2sinΘcosΘ)/g
Maximum Height reached: H = V02sin2Θ0/2g
Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)
Expand your confidence, grow study skills and improve your grades.
Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.
Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with a tutor at www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology. Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.
Free to know our price and packages for online physics tutoring. Chat with us or submit request at [email protected]
tutorsglobe.com wave nature of electrons assignment help-homework help by online atomic structure tutors
build up the layout of a lap winding for a 3 phase ac machine comprising 4 pole and 24 slots. there are 2 coil sides per slot.
www.tutorsglobe.com offers balance sheet homework help, balance sheet assignment help, balance sheet solutions, answering questions to balance sheet, accounting tutoring by qualified tutors.
Derivatives of Monosaccharides tutorial all along with the key concepts of Types of Sugar derivatives, Sugar alcohols, Amino sugars, Uronic acids, N-acetylneuraminic acid, Reactions of Monosaccharides and Configuration of Glucose
The method of superimposing (mixing) signal wave on the carrier wave is termed as modulation.
Lagrange and Hamiltonian Mechanics tutorial all along with the key concepts of Frame of Reference and Constraints of Motion, Constraints of Motion, Generalized Coordinates and Degrees of Freedom
tutorsglobe.com polypetalous and irregular assignment help-homework help by online forms of corolla tutors
www.tutorsglobe.com offers thiols & sulfides homework help, thiols & sulfides assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
tutorsglobe.com laboratory diagnosis of infections assignment help-homework help by online streptococcus pyogenes tutors
www.tutorsglobe.com offers ethane homework help, ethane assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
tutorsglobe.com bulb assignment help-homework help by online propagation by underground stem tutors
Is your academic task driving you insane? Avail top-rated Hinduism Assignment Help at low price and score well.
www.tutorsglobe.com offers substitution of the hydroxyl group homework help, assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
the working of the table fan is that they do not in fact decrease the temperature of the room but due the circulation and wind motion they effect in surface cooling and provide a breezy feeling.
www.tutorsglobe.com offers Module Based Programming Languages homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
1948393
Questions Asked
3689
Tutors
1476524
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!