Note that in the document cited, they make the assumption that the air is not moving, and begun their derivation from $f = Dv^2$, and this $v$ was relative to the air and therefore the following equations simply used the velocity of the ball. However, for a general estimation, you can use the relatively simple methods described in this document to begin calculating the effects of air drag on projectiles. The values of the radius of the object, its mass, its initial velocity and angle, the wind velocity and angle, and dt can all be entered by the user, and the values of wind angle and wind velocity are defaulted to 0, the angle is defaulted to 45 degrees, and dt is defaulted to 0.001, although these values can be changed by the user whenever they desire.Īs mentioned in the comments, this is an extremely complex problem if you intend to consider every possible aspect. Instead, I will need to create a small time step, dt, and plot the points at each time step over a certain interval. As this is being written in a computer program (python 2.7.3, to be exact), I cannot perform any integration or differentiation of the functions. Any help at all here would be very much appreciated, but if possible, could whoever responds please try to address all of my questions, numerous though they are? Sorry, I know I'm asking a lot, it's just that I really want to understand the principles behind this. I would naturally have a constraint on the wind velocity so that the object would always inevitably hit the ground, so the force of the wind in the y-direction, if it were blowing upwards, would have to be less than the force of gravity of the object, so that it still fell.
#Physics calculator projectile motion how to#
So I guess another request is an explanation of how to obtain the set of equations (position, velocity, acceleration) for the x direction based on whether the wind angle is helpful or hurtful, and how to obtain the set of equations for the y direction, based again on whether the wind is helpful or hurtful.
Oh, and in the scenario of the wind, it can blow from any angle, which means it will affect the x and y velocities and either augment them or lessen them depending on the angle at which it blows. The reason I want to know this is that I am writing a program to model this behavior, but I first need to know these equations.Īlso, if possible, could someone provide some help on finding equations for the maximum height the projectile reaches, as well as the distance it travels before it hits the ground? I would like both of these to be values the user of the program can find if desired. In essence, what I would like to know is how to rewrite the kinematics equations to take into account the air resistance and moving wind and the terminal velocity. If an object were fired out of a cannon, or some sort of launcher, so that it had both an initial velocity and an initial angle, and air resistance is taken into account, what would be the equations for the x and y components of the position, velocity, and acceleration.įurthermore, I am wondering how these equations would change if there were also a wind blowing at an angle.
Maximum Height.I am wondering how the general kinematics equations would change in the following situation. 3.3: Projectile Motion - Physics LibreTexts. Equation 2 shows that for a given projectile velocity vo, R is maximum when sin2θo is maximum, i.e. If you use the vertical component of its initial speed, you can write underbrace (v_"h max"^2)_ (color (blue) ("=0")) = v_text (0y)^2 - 2 * g * h_"max" This is equivalent to v_ (0y)^2 = 2 * g * h_"max" The maximum … Maximum Height, Time of Flight and Horizontal Range. … How do you determine the maximum height of a projectile?. Online physics calculator to calculate the maximum height of projectile based on the law of physics. Maximum Height of a Projectile Calculator. Projectile height calculator | Math Methods.
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