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 is trajectory calculated?
So, the final trajectory formula may be expressed as: y = h + x * tan(α) – g * x² / (2 * V₀² * cos²(α))
Is 45 degrees the best angle of trajectory with air resistance?
The sine function reaches its largest output value, 1, with an input angle of 90 degrees, so we can see that for the longest-range punts 2θ = 90 degrees and, therefore, θ = 45 degrees. A projectile, in other words, travels the farthest when it is launched at an angle of 45 degrees.
How do you find distance with air resistance?
1 Answer
- As mentioned in the comments, the resistive force is proportional to the velocity and let the constant of proportionality be b.
- SO, ma=mg−bv.
- a=g−bvm.
- Let b/m=k.
- Then a=g−kv.
- dv/dt=g−kv.
- This is a linear differential equation. Solving this for v in terms of t, we get.
- Applying the condition v=0 at t=0, we get c=−g/k.
Why is 45 degrees the best launch angle without air resistance?
As ball speed increases, so does the drag force and the lower is the required launch angle. A launch at 45 degrees would allow the ball to remain in the air for a longer time, but it would then be launched at a lower horizontal speed at the start and it would slow down more because of the longer flight time.
What is the best angle to launch a projectile with air resistance?
For ideal projectile motion, which starts and ends at the same height, maximum range is achieved when the firing angle is 45°. If air resistance is taken into account, the optimal angle is somewhat less than 45° and this is often considered obvious.
How do you find velocity with air resistance?
The net external force is equal to the difference between the weight and the drag forces (F = W – D). The acceleration of the object then becomes a = (W – D) / m . The drag force depends on the square of the velocity. So as the body accelerates its velocity (and the drag) will increase.
What is air resistance of the projectile?
Suppose, further, that, in addition to the force of gravity, the projectile is subject to an air resistance force which acts in the opposite direction to its instantaneous direction of motion, and whose magnitude is directly proportional to its instantaneous speed.
What is the trajectory of projectile?
The trajectory of a projectile is a parabola. Projectile motion is a form of motion where an object moves in a bilaterally symmetrical, parabolic path. The path that the object follows is called its trajectory.
How many types of trajectories are there?
Examples of the three different types of trajectories present in the photoionization process: 1HCNT (dashed blue line), 1HCRT (solid red line), and 2HCT (solid gray line).
What are types of trajectory?
Types of trajectories include:
- trajectory of a projectile. lofted trajectory, a particular type of non-minimum energy ballistic trajectory.
- trajectory (fluid mechanics), the motion of a point in a moving fluid.
- in motion planning, the trajectory of a robotic motion.
- phase space trajectories of dynamical systems.