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I am trying to graph a projectile through time at various angles. The angles range from 25 to 60 and each initial angle should have its own line on the graph.

The formula for "the total time the projectile is in the air" is the formula for t. I am not sure how this total time comes into play, because I am supposed to graph the projectile at various times with various initial angles. I imagine that I would need x,x1,x2,x3,x4,x5 and the y equivalents in order to graph all six of the various angles. But I am confused on what to do about the time spent. You know this already, but lets take a second and discuss something.

What do you need to know in order to get the trajectory of a particle? Initial velocity and angle, right? Initial is important! That's the time when we start our experiment. So time is continuous parameter! You don't need the time of flight. Firstly, less of a mistake, but matplotlib.

Secondly, your angles are in degrees, but math functions by default expect radians. You have to convert your angles to radians before passing them to the trigonometric functions. Thirdly, your current code sets t1 to have a single time point for every angle.

This is not what you need: you need to compute the maximum time t for every angle which you did in tthen for each angle create a time vector from 0 to t for plotting! Lastly, you need to use the same plotting time vector in both terms of ysince that's the solution to your mechanics problem:. This assumes that g is positive, which is again wrong in your code.

### Plotting Trajectory Of Projectile

Unless you set the y axis to point downwards, but the word "projectile" makes me think this is not the case. I made use of the fact that plt. I also used [None,:] and [:,None] to turn 1d numpy array s to 2d row and column vectors, respectively. By multiplying a row vector and a column vector, array broadcasting ensures that the resulting matrix behaves the way we want it i. Learn more. Asked 4 years, 4 months ago. Active 4 years, 4 months ago.

Viewed 14k times. Also, no need to cast t to a np. Active Oldest Votes.Hot Threads. Featured Threads.

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### Projectile Motion Calculator and Solver

For a better experience, please enable JavaScript in your browser before proceeding. Linearizing a parabolic graph of a projectile motion. Thread starter OhyesOhno Start date Aug 21, Homework Statement How do you linearize a parabolic graph? Angle tan Average Displacement The equation of the parabola is found to be: Funny, I was just helping a friend with the same thing. Redbelly98 Staff Emeritus. Science Advisor. Homework Helper. Insights Author. There are two things people mean when they say "linearize" a graph or data.

As Topher said: approximate the graph as-is with a straight line. What I think OhyesOhno means: transform the data so that the graph really is a straight line.Vector Addition Two vectors can be added using the triangle or parallelogram method.

Vector Addition and Subtraction Two vectors can be added or subtracted. Vector Components The horizontal and vertical components of any vector can be shown.

Vector Addition and Subtraction Practice Practice vector addition and subtraction. Uniform Acceleration in One Dimension: Motion Graphs This simulation is intended to help students get a better understanding of the relationships between various quantities involved in uniformly accelerated motion.

By adjusting the sliders or input boxesa student can change the initial position, the initial velocity, and the acceleration of an object, and can observe how each change affects the graphs of position, velocity, and acceleration vs.

Position, Velocity, and Acceleration vs. Time Graphs In this simulation you adjust the shape of a Velocity vs. Time graph by sliding points up or down. The corresponding Position vs. Time and Acceleration vs. Time graphs will adjust automatically to match the motion shown in the Velocity vs. Time graph. Kinematics Graphs: Adjust the Acceleration This is a simulation that shows the position vs.

Students can adjust the initial position and initial velocity of the objects, and then adjust the acceleration of the object during the four time intervals represented on all the graphs. Time Graphs This simulation shows the velocity vs. Adjust the velocities by sliding the blue points up or down. Adjust the total time interval by sliding the red dots horizontally.

Uniform Acceleration in One Dimension This is a simulation of the motion of a car undergoing uniform acceleration. The initial position, initial velocity, and acceleration of the car can be adjusted.

You can adjust the initial position, initial velocity, and acceleration of each of the cars. When the run button is pressed, you can watch an animation of the motion of the cars and also see the position vs. Projectile Motion Explore projectile motion by changing the initial conditions and watching the resulting changes in the projectile's motion. Exploring Projectile Motion Concepts Using this simulation, students can explore various types of projectile motion.

Four projectiles are launched over level ground at angles of 20, 30, 45, and 60 degrees. You have the option of setting them all to have the same horizontal range, the same maximum height, or the same initial velocity.Consider a spherical object, such as a baseball, moving through the air. The motion of an object though a fluid is one of the most complex problems in all of science, and it is still not completely understood to this day.

One of the reasons this problem is so challenging is that, in general, there are many different forces acting on such objects, including:.

In most introductory physics and dynamics courses, gravity is the only force that is accounted for this is equivalent to assuming that the motion takes place in a vacuum. Here we will consider realistic and accurate models of air resistance that are used to model the motion of projectiles like baseballs. The drag force is always directly opposed to the velocity of the object. The free body diagram for a baseball subject to gravity and air resistance. Observe that the drag due to air resistance is always in the opposite direction to the velocity.

Image credit: Microsoft clip art. The Reynolds number gives a ratio between inertial forces and viscous forces in a fluid flow. For very small Reynolds numbers, the viscous forces are much stronger than the inertial forces think of trying to stir a cup of honey.

For very large Reynolds numbers, the viscous forces are negligible, and we refer to the flow as inviscid think of stirring a cup of coffee. An important result in fluid dynamics is that the drag coefficient is a function only of the Reynolds number of the fluid flow about the object. However, the relationship has been established numerically based on experimental data.

See Figure aft-fd for a schematic diagram of the drag coefficient's dependence on the Reynolds number. Experimental dependence of drag coefficient on Reynolds number for a sphere. This is referred to as quadratic dragbecause the drag force magnitude is proportional to the square of the speed. Below is an interactive graphic showing the trajectory of an object with gravity and quadratic drag. Trajectories of a projectile in a vacuum blue and subject to quadratic drag from air resistance red.

There is no well-measured record for longest baseball home run. Home Reference Applications. Projectiles with air resistance Consider a spherical object, such as a baseball, moving through the air. One of the reasons this problem is so challenging is that, in general, there are many different forces acting on such objects, including: gravity drag lift thrust buoyancy bulk fluid motion, such as wind inertial forces, such as the centrifugal and Coriolis forces In most introductory physics and dynamics courses, gravity is the only force that is accounted for this is equivalent to assuming that the motion takes place in a vacuum.

Position, velocity, and acceleration Kinetics of point masses. Drag forces and drag coefficients The drag force is always directly opposed to the velocity of the object.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information.

I am trying to graph a projectile through time at various angles. The angles range from 25 to 60 and each initial angle should have its own line on the graph. The formula for "the total time the projectile is in the air" is the formula for t. I am not sure how this total time comes into play, because I am supposed to graph the projectile at various times with various initial angles.

I imagine that I would need x,x1,x2,x3,x4,x5 and the y equivalents in order to graph all six of the various angles. But I am confused on what to do about the time spent. You know this already, but lets take a second and discuss something. What do you need to know in order to get the trajectory of a particle? Initial velocity and angle, right? Initial is important! That's the time when we start our experiment.

So time is continuous parameter! You don't need the time of flight. Firstly, less of a mistake, but matplotlib. Secondly, your angles are in degrees, but math functions by default expect radians. You have to convert your angles to radians before passing them to the trigonometric functions. Thirdly, your current code sets t1 to have a single time point for every angle.

This is not what you need: you need to compute the maximum time t for every angle which you did in tthen for each angle create a time vector from 0 to t for plotting! Lastly, you need to use the same plotting time vector in both terms of ysince that's the solution to your mechanics problem:. This assumes that g is positive, which is again wrong in your code. Unless you set the y axis to point downwards, but the word "projectile" makes me think this is not the case.

I made use of the fact that plt. I also used [None,:] and [:,None] to turn 1d numpy array s to 2d row and column vectors, respectively. By multiplying a row vector and a column vector, array broadcasting ensures that the resulting matrix behaves the way we want it i. Learn more. Asked 4 years, 4 months ago.

Active 4 years, 4 months ago. Viewed 14k times. Also, no need to cast t to a np.Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectileand its path is called its trajectory. The motion of falling objects, as covered in Problem-Solving Basics for One-Dimensional Kinematics, is a simple one-dimensional type of projectile motion in which there is no horizontal movement.

The most important fact to remember here is that motions along perpendicular axes are independent and thus can be analyzed separately. This fact was discussed in Kinematics in Two Dimensions: An Introductionwhere vertical and horizontal motions were seen to be independent.

The key to analyzing two-dimensional projectile motion is to break it into two motions, one along the horizontal axis and the other along the vertical. This choice of axes is the most sensible, because acceleration due to gravity is vertical—thus, there will be no acceleration along the horizontal axis when air resistance is negligible. As is customary, we call the horizontal axis the x -axis and the vertical axis the y -axis.

The magnitudes of these vectors are sxand y. Note that in the last section we used the notation A to represent a vector with components A x and A y. If we continued this format, we would call displacement s with components s x and s y. However, to simplify the notation, we will simply represent the component vectors as x and y.

Of course, to describe motion we must deal with velocity and acceleration, as well as with displacement. We must find their components along the x — and y -axes, too. We will assume all forces except gravity such as air resistance and friction, for example are negligible.

Note that this definition assumes that the upwards direction is defined as the positive direction. If you arrange the coordinate system instead such that the downwards direction is positive, then acceleration due to gravity takes a positive value.

Both accelerations are constant, so the kinematic equations can be used. Figure 1. The total displacement s of a soccer ball at a point along its path. The vector s has components x and y along the horizontal and vertical axes. Step 1. Resolve or break the motion into horizontal and vertical components along the x- and y-axes.

The magnitude of the components of displacement s along these axes are x and y.

## Projectile Motion Calculator

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:. Step 3.Your browser seems to have Javascript disabled. We're sorry, but in order to log in and use all the features of this website, you will need to enable JavaScript in your browser.

We can describe vertical projectile motion through a series of graphs: position, velocity and acceleration versus time graphs. Therefore, everything you learnt about the graphs describing rectilinear motion is applicable when describing vertical projectile motion. As a reminder, here is a summary table, from Grade 10 rectilinear motion, about which information we can derive from the slope and the area of various graphs:.

The graphs are the graphical representations of the equations of motion. This means that if you have the graph for one of position, velocity or acceleration you should be able to write down the corresponding equation and vice versa.

The type of graphs is related to the equation of motion: position is a parabola, velocity is a straight line and acceleration is a constant. The characteristic features then depend on the sign convention and the specific values of the problem. We have to choose a positive direction as before.

We choose upwards as positive. The position versus time graph for the motion described is shown below:. Whether it is an upward or downward shift will depend on which directionwas chosen as the positive direction. The magnitude of the shift will depend on the choice of origin for thecoordinate system frame of reference. Note that we chose upwards as our positive direction therefore the acceleration due to gravity will be negative. The slope i. The final plot is a graph of acceleration versus time, and is constant because the magnitude and direction of the acceleration due to gravity are constant.

Cases 2 and 3: Initial velocity zero or downwards We start by choosing a direction as the positive direction. We want to compare the graphs with the first case, so we will choose the same direction upwards to be the positive direction.

If an object starts from rest for example is droppedthen the initial velocity is zero. We know that there is constant acceleration and hence the graph of velocity versus time looks like this:.

It is important to notice that the slope of all the velocity versus time graphs has the same magnitude. If the same direction is chosen as positive then the slope has the same magnitude AND the same sign direction. The magnitude of the slope of the graph is the magnitude of the acceleration. For motion with an initial velocity in the negative direction, the graph of displacement versus time will be a narrower parabola as compared to the case where the object falls from rest. This is shown in this graph where the initial velocity is in the negative direction:.

You may be wondering if the final position is always the same as the initial position, as we had for our Case 1 example. That is not necessarily true.

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