Our projectile motion calculator is a tool that helps you analyze the parabolic projectile motion. It can find the time of flight, but also the components of velocitythe range of the projectile, and the maximum height of flight.

Continue reading if you want to understand what is projectile motion, get familiar with the projectile motion definition, and determine the abovementioned values using the projectile motion equations. Imagine an archer sending an arrow in the air. It starts moving up and forward, at some inclination to the ground. The further it flies, the slower its ascent is — and finally, it starts descending, moving now downwards and forwards and finally hitting the ground again.

If you could trace its path, it would be a curve called a trajectory in the shape of a parabola. Any object moving in such a way is in projectile motion. Only one force acts on a projectile — the gravity force. Air resistance is always omitted. If there were any other forces acting on the body, then — by projectile motion definition — it wouldn't be a projectile. Projectile motion is pretty logical. Our projectile motion calculator follows these steps to find all remaining parameters:.

If the vertical velocity component is equal to 0, then it's the case of horizontal projectile motion. Flight ends when the projectile hits the ground. We can say that it happens when the vertical distance from the ground is equal to 0. Then, from that equation, we find that the time of flight is.

After solving this equation, we get:. The range of the projectile is the total horizontal distance traveled during the flight time. Things are getting more complicated for initial elevation differing from 0. Then, we need to substitute the long formula from the previous step as t :.

Uff, that was a lot of calculations! Let's sum that up to form the most essential projectile motion equations:. Using our projectile motion calculator will surely save you a lot of time. It can also work 'in reverse'. For example, enter the time of flight, distance, and initial height and watch it do all calculations for you! Noprojectile motion and its equations cover all objects in motion where the only force acting on them is gravity.

This includes objects that are thrown straight upthose thrown horizontallythose that have a horizontal and vertical componentand those that are simply dropped. Objects with projectile motion include: keys being thrown, a kg projectile being thrown 90 m by a trebucheta football being kicked so that it no longer touches the ground, a diver jumping from a diving board, an artillery shell the moment it leaves the barrel, and a car trying to jump a bridge.

There is only one force acting on a projectile - gravity. This means that an object will eventually fall to Earth. But what about if the object is moving so fast horizontally that, by the time it reaches the ground, the ground is no longer there? This is the principle that governs satellites.

There is only one force acting on an object in projectile motion - gravity. This means that any change in vertical speed is due to gravitational acceleration, which is 9.

In the horizontal direction, there is no change in speed, as air resistance is assumed to be negligibleso acceleration is 0.

Initial velocitythe initial height the projectile is being launched from, and gravity will all affect a projectile launched horizontally. Air resistance will also have an effect in real life, but for most theoretical calculations it is negligible and is therefore ignored.Sitting before you is a model rocket of your very own design. Everything from the rocket fuselage to the parachute was designed by you and you couldn't be prouder.

The custom paint job turned out better than expected and the shining exterior brings a tear to the eye. To quote Keats, "a thing of beauty is a joy forever. That's an important question, since a beautiful model rocket that doesn't fly can be a huge letdown! You want your rocket to soar to the heavens! You want to touch the clouds and challenge the gods!

Well, maybe that's a little melodramatic, but you want your rocket to perform just as well as it looks. To measure how well your rocket flies, you'll need to know how to measure the apogee of its flight. In rocketry, the apogee is defined as the highest point of the rocket's flight.

So, how do you go about measuring this point? Model rockets can travel for hundreds or even thousands of feet up in the air, so how on earth can we measure their maximum altitude? Fortunately, there are several methods for doing this and I'll explain a few of my favorites here. Okay, so using an electronic altimeter isn't really "cheating," but it takes some of the fun out of calculating altitude with hand tools and mathematics.

Nevertheless, electronic altimeters can save rocket enthusiasts a lot of time and hassle. The weight and size shouldn't be an issue for a large rocket, but a small rocket like the Estes Quark probably wouldn't be a good candidate for an electronic altimeter. Also, if you're prone to losing rockets to trees, lakes, or shotgun-wielding neighbors kiddingyou might want to find a less expensive method of calculating altitude. The concept behind the streamer method is that a streamer of plastic with fixed dimensions attached to a small weight will fall at a reasonably constant velocity.

The large surface area of the streamer creates a lot of wind resistance or drag and the weight will quickly reach its terminal velocity. The weight has a mass of three grams and the dimensions of the polyethylene streamer are 12" x 1" x 0. A streamer of this size and mass will fall with a terminal velocity of approximately 18 feet per second.

Of course, it's possible to experiment with different weights and streamers. All you need is your custom streamer and a very tall place to test it! Once you know the terminal velocity of the streamer, you can calculate altitude simply by multiplying the velocity by the time it took the ejected streamer to fall to earth.

The streamer itself would be placed in the model rocket above the parachute or recovery system. For tumble recovery rockets like the aforementioned Quarkyou might not have room for a streamer, which leads us to our next method.

So far, small rockets have proven troublesome in our desire to measure altitude. They're too small for an electronic system and they're too small to carry a streamer payload. To track something like the Quark, we'll need to use optical tracking. There are several methods of optical tracking and I'll discuss the simplest one here.

Be forewarned, however. There's going to be some math up ahead. Remember when you were a kid and you wanted to know when you were ever going to use trigonometry? Well buddy, here it is. The quickest and easiest way to determine your rocket's altitude with optical tracking is to use elevation-angle-only tracking.

This is a very simple method and the amount of trigonometry isn't nearly as bad as I made it out to be. Let's begin with a diagram of the launch site. If we assume that the rocket travels reasonably straight up from the launchpad, then we can draw ourselves a nice right triangle. If you're using a calculator, make sure you're in degree mode and not radian mode.

Of course, this is assuming you measured the angle in degrees, although I don't think I've ever met anyone who measured rocketry angles in radians.Equations for model rocketeers - how to accurately predict speed and altitude for your rocket from weight, diameter, motor thrust and impulse. There are three basic equations to find the peak altitude for your rocket they are also summarized here :. All the weird terms in these equations are explained in the following section on the method for using the equations.

Good you asked. Two things will cause a difference between your calculation and where your rocket actually goes. A rocket will vary in its performance for three main reasons:. Secondlythe equations make some approximations. I've minimized these as much as possible, as you will see. The three biggest approximations are. In the example above I hand-waved the value I use for motor mass, but in reality I'm very deliberate about the value I choose.

As your rocket burns fuel, the mass of the rocket changes. I estimate the mass of the rocket during the boost phase by adding. The empty weight of the rocket is given to you as part of its specifications. You can also get the numbers on motor mass and propellant mass from the catalogs the Estes or Aerotech catalog has their's, for instance or you can estimate them as follows:. For fast estimation of high power AP motors in the field I have a cool cheat - the fully loaded motor mass in grams is roughly the same as the motor impulse in Newton-seconds.

The propellant weight is roughly half the loaded motor weight. For Blackjacks add grams. For black powder Estes motor casings, I use a ballpark value of 0. I believe that's plenty good enough. So to get the mass of propellant just divide the impulse bywhich gives it to you in kg.

Multiply this number by Of course, the easy way is to get the numbers from the catalog. Remember since you are burning the propellant up during the boost phase, use half the calculated propellant mass as an average value. Note: if you've done any reading on rocket physics, then just plugging in an average value for the rocket mass should seem like an awful idea.

THE rocket equation is derived by calculating exactly the effect of this changing mass. By contrast, the propellent for the space shuttle is 25 times the payload weight, and the changing mass cannot be approximated by an average value. For typical model rockets, this approximation leads to an error of less than one percent, and allows us then to use an expression that accounts for wind resistance, a much more important factor. That in fact is the secret to the accuracy of these equations.

## A toy rocket starts from rest on the ground and then accelerates at 39.2 m/s^2 (up) for 5.0s.?

Oh, yeah, that's an easy calculation now. The time from burn-out to apogee high point we will call ta. To find it just calculate:. This is the time from burnout to apogee and should correlate closely with the delay time on the ejection charge on your engine. For total time launch to apogee, add burn time t and ta. Since I posted the derivation of these equations I've received a very nice much prettier version in PDF format from Dr.

Christian Strutz in Germany which you can get. When this expression is substituted into the above Second Law equations, they become intractable and must be solved with numerical methods.When you launch a projectile into the air, you can use physics to determine how long it will remain airborne. Because the force of gravity only acts downward — that is, in the vertical direction — you can treat the vertical and horizontal components of the flight path separately. As a result, you can calculate things like the time the projectile will be airborne before it strikes the ground.

Say, for example, that you decide to shoot a cannon into the air. How long do you have to get out of the way before the cannonball comes back down and obliterates your new cannon? First, you have to determine how long it will take for the cannonball to reach its maximum height. It takes about 88 seconds for the cannonball to reach its maximum height ignoring air resistance.

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So how long will it take the cannonball to complete its entire trip? Flights like the one taken by the cannonball are symmetrical; the trip up is a mirror of the trip down. The velocity at any point on the way up has exactly the same magnitude as on the way down, but on the way down, the velocity is in the opposite direction.

This means that the total flight time is double the time it takes the cannonball to reach its highest point, or. You have seconds, or 2 minutes and 56 seconds, until the cannonball destroys the cannon that fired it.The maximum height calculator is a tool for finding the maximum vertical position of a launched object in projectile motion.

Whether you need the max height formula for an object starting directly off the ground or from some initial elevation - we've got you covered. If you're still wondering how to find maximum height of a projectile, read the two short paragraphs below, and everything should become clear. Maximum height of the object is the highest vertical position along its trajectory.

The object is flying upwards before reaching the highest point - and it's falling after that point. From that equation we can find the time th needed to reach the maximum height hmax :. And what if we launch a projectile from some initial height h?

No worries! Apparently, the calculations are a piece of cake - all you need to do is add this initial elevation! Also, you may want to have a look at our even more accurate equivalent - the free fall with air resistance calculator. Embed Share via. Angle of launch.

### How to Calculate How Long a Projectile Is Airborne

Initial height. Maximum height. Advanced mode. Belt length. Normal force. Projectile motion. Table of contents: How to find the maximum height of a projectile? Maximum height calculator helps you find the answer. How to find the maximum height of a projectile?

Maximum height calculator helps you find the answer Just relax and look how easy-to-use this maximum height calculator is: Choose the velocity of the projectile.

Enter the angle. Optionally, type the initial height. In our case, our starting position is the ground, so type in 0. Can the ball fly over a ft fence? Here it is - maximum height calculator displayed the answer! It's So it will not fly over the mentioned barrier - throw it harder or increase the angle to reach your goal. Just remember that we don't take air resistance into account!The height h in ft.

Username: Password: Register in one easy step! Reset your password if you forgot it. Solvers Solvers. Lessons Lessons. Answers archive Answers. When will the rocket reach the ground? When will the rocket reach its maximum height. What is the maximum height of the rocket? Greaph this situation f.

State the domain and range of the graph? I'm lost after that. Your work: or or So far, so good. Remember the rocket goes up, and then comes back down again. What you have discovered so far is that the height is feet 3 seconds after launch, and then it keeps going up. At some point it starts coming back down again, and at 11 seconds after launch it passes feet again. Part b is exactly the same problem, except that you use 0 instead of You will get two roots for your equation again, one will be 0 because the rocket is on the ground at time 0, and the other will be the time it hits the ground on the way back down.

Part c. Recognize that h t will graph as a parabola, concave down. That means the vertex of the parabola is a maximum value. The x-coordinate of the vertex of a parabola expressed in the form is given byso in your case.

So maximum height will be reached at 7 seconds. Note that this makes sense because 7 seconds is exactly in the middle of the 3 seconds and 11 seconds you calculated in part a.

This gives you a check on your work in part b, because 7 must also be exactly in the middle of 0 and whatever you got from part b. Part d. Simply evaluate h 7in other words calculate Part e. Part f. The domain of the function h t as stated is all real numbers, but in practical terms, the function is undefined both before the rocket is launched t.

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