 Interesting properties of projectile motion

This java applet let you play with projectile motion.

There are two case you can play with :

1. look at trajectories of many projectile with the same initial speed :
The red half circle is proportional to the speed of all the projectiles.
You can click near the red curve with left mouse button and drag the mouse button to change the speed of the projectiles. ( or enter value into speed=xxx box)
The number of the projectile is shown as count= xxx.

What is the meaning of the green ellipse trace? I will let you find out by yourself.

Press the Start button, all the projectiles will spread out.

At any instance, the trajectory of all the projectiles is an arc of a circle.

Would you like to calculate the equation for that circle?
The center of the circle moving down with velocity v=gt (g:gravity field strength, t: time)
The radius of this circle r = v t .
It will be easier if you treat the projectile's motion as
a constant motion + free fall (as case 2 for this applets).
Remind you again! What is the meaning of the green ellipse trace?
Why not calculate the equation for that ellipse!
When the animation is suspended:
The envelope of all the trajectories Is a parabola.
If you are not within the region enclosed by the parabola, then you are safe.
Can you think of any application for this curve?

Click the mouse button to suspend the animation, click it again to resume.
Press Reset button for default values.( now you can change the speed by mouse)
What will happen with different initial speed?

2. Let us select case 2 to study the motion of a projectile. ( independence )
Yellow circle is the starting point of a projectile.
You can click the mouse at that location and drag the mouse to change it.
The red arrow represents the initial speed of the projectile.
You can click near the tip of the arrow,
with left mouse button and drag it to change the speed.(same direction)
with right mouse button and drag it to change the direction.(same speed)
The gray line is the trajectory for the object without gravity.
The parabola is the trajectory for the object with gravitational field.

The vertical distance between the above curve is the free fall distance at that moment.
The blue circle is the range when it is fired from the ground level.
Press Start to shoot the object(yellow) according to the initial conditions. At the same time,

A green circle is released at the same location with any initial velocity. (free fall)
Another red circle is moving with constant velocity (without gravity)
The gray circles will also be released along the path,
and meet with the yellow circle.
 displacement of red circle + displacement of green circle  = displacement of yellow circle Constant motion + Free fall = Projectile motion
Enjoy this java applet and learn some physics!