How do you calculate projectile motion with air resistance?

Mathematically, the resistive force represented by the vector F can be written as F=-f(v) u, where u=V/|V| is the unit vector along the direction of the velocity V. The minus sign guarantees that the air resistance acting on the projectile is always opposite to the direction of its velocity.

How does air resistance affect trajectory?

Because air resistance affects the horizontal component of a projectiles trajectory, the effect of it can be minimized by lowering the angle of release. Speed or velocity is directly related to distance. The greater the speed of release, the greater the distance covered in flight.

How do you calculate air resistance?

The units for the force of air resistance are in Newtons (N). Air resistance can be calculated by taking air density times the drag coefficient times area all over two, and then multiply by velocity squared.

Does air resistance affect acceleration?

With air resistance, acceleration throughout a fall gets less than gravity (g) because air resistance affects the movement of the falling object by slowing it down. How much it slows the object down depends on the surface area of the object and its speed.

Does air resistance increase with speed?

Air resistance is the result of collisions of the object’s leading surface with air molecules. Increased speeds result in an increased amount of air resistance. Increased cross-sectional areas result in an increased amount of air resistance.

How does air resistance affect distance?

Objects moving through air are slowed down due to air resistance, sometimes called drag. This air resistance affects a spacecraft when it re-enters the Earth’s atmosphere but also the path of a projectile such as a bullet or a ball. The maximum height, the range and the velocity of the projectile are all reduced.

What factors affect air resistance?

The amount of air resistance an object experiences depends on its speed, its cross-sectional area, its shape and the density of the air. Air densities vary with altitude, temperature and humidity.

How do you calculate trajectory height?

h = v 0 y 2 2 g . This equation defines the maximum height of a projectile above its launch position and it depends only on the vertical component of the initial velocity.

What happens if there is no air resistance?

If there is no air resistance, after you let go of an object the only force on it is the gravitational force. The gravitational force is proportional to the mass of the object. The acceleration of an object is proportional to the net force on the object and inversely proportional to the mass of the object.

How do you minimize air resistance?

Two ways to reduce air resistance are stated: reducing the area in contact with air (by the cyclist ducking down or cycling behind someone else) and by being more streamlined (wearing smoother surfaces or a more streamlined helmet).

How is the trajectory of a projectile affected by air resistance?

Furthermore, there is always an initial time interval during which the trajectory is identical to that calculated in the absence of air resistance ( i.e., ). Finally, in the presence of air resistance, the projectile tends to fall more steeply than it rises.

Is there a formula to calculate projectile trajectory?

So there is no formula for the trajectory. It is possible, of course to obtain a numerical solution of the differential equation and calculate the trajectory ( and that is what is done by e.g. artillery officers when they want to know the exact elevation and azimuth they should set their cannons to hit a given target).

How is the trajectory of an object determined?

A ballistic trajectory is the path of an object that is dropped, thrown, served, launched, or shot but has no active propulsion during its actual flight. Consequently, the trajectory is fully determined by a given initial velocity and the effects of gravity and air resistance.

Which is an example of a ballistic trajectory?

Consequently, the trajectory is fully determined by a given initial velocity and the effects of gravity and air resistance. Mortars, bullets, particles, and jumping computer game characters (between key presses) are all examples of ballistics, while actively controlled aircraft and rocket-propelled grenades are not.