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 practical application of genetic transformation assignment help-homework help by online transgenic plants tutors
Plant-Water Relations tutorial all along with the key concepts of Cellular water relations, Stomatal mechanism, Transpiration process and Water translocation
bluetooth is a standard communications protocol mainly designed for low power consumption, along with a short range (see table below). since the devices make use of a radio (broadcast) communications system.
tutorsglobe.com clinical manifestations assignment help-homework help by online cryptococcus neoformans tutors
tutorsglobe.com laboratory diagnosis of shigella assignment help-homework help by online shigella tutors
tutorsglobe.com process of urea assignment help-homework help by online urea cycle tutors
If the machines or appliances are not working on providing electrical energy, it is needed to perform some test to make out the fault.
tutorsglobe.com colour television assignment help-homework help by online tv principle tutors
Structure and Function of Plant Cells tutorial all along with the key concepts of Membrane System, Organelles for Energy Conversion, Cell Movement, Chloroplasts, Mitochondria, Endoplasmic Reticulum, Dictyosomes, Vacuoles and Micro Bodies
total number of coils =24/4= 6; coils per phase =12/3= 4; number of coils of groups per phase = 3 x 2 = 6
tutorsglobe.com hydrophytes-mesophytes-xerophytes assignment help-homework help by online environmental biology tutors
tutorsglobe.com timber yielding plant–teak assignment help-homework help by online economic importance tutors
theory and lecture notes of electromagnetic induction all along with the key concepts of magnetic fields, current carrying conductors, magnetic flux , fleming’s left and right hand rule, electromagnetic induction. tutorsglobe offers homework help, assignment help and tutor’s assistance on theory of electromagnetic induction.
tutorsglobe.com culture development assignment help-homework help by online microbial culture tutors
Transmission and Expression of Characters tutorial all along with the key concepts of Transmittable traits in Humans, Transmittable traits in Plants, Applications of Transmission of Factors, Application of Genetic to Agriculture
1948590
Questions Asked
3689
Tutors
1478416
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!