Projectile Motion in Cocos2d iphone - iphone

Question

I want to throw a ball that has a projectile motion. I have a monkey on centre of screen and onTouchBegin I am taking the starting point of the touch and onTouchEnded I am taking the ending points. From the starting and ending points I am taking the angle value between them. Like 30 degrees, 45 or 90 degree.
This is my code by which I have calculated angle of start to endpoint
float angleRadians = atan2(startTouchPoint.x - touchPoint.x, startTouchPoint.y - touchPoint.y);
float angleDegrees = CC_RADIANS_TO_DEGREES(angleRadians);
float cocosAngle = -1 * angleDegrees;
Now i am using Projectile motion formula to throw ball with angle i have calculated from above formula .
inside init method
gravity = 9.8; // metres per second square
X = 0;
Y = 0;
V0 = 50; // meters per second -- elevation
VX0 = V0 * cos(angle); // meters per second
VY0 = V0 * sin(angle); // meters per second
gameTime = 0;
and onTouchEnded i have called fire method which will throw ball .
-(void)fire:(ccTime) dt
{
CCLOG(#"Angle 1: %.2f",angle);
gameTime += dt*6;
// x = v0 * t * cos(angle)
X = (V0 * gameTime * cos(angle))/2+120;
// y = v0 * t * sin(angle) - 0.5 * g * t^2
Y = (V0 * gameTime * sin(angle) - 0.5 * gravity * pow(gameTime, 2))/2+255;
if (Y > 50)
{
sprite_webfire.position = ccp(X,Y);
flag = true;
}
else
{
//angleValue += 15;
angleValue = angle;
angle = [self DegreesToRadians:angleValue];
gravity = 9.8; // metres per second square
X = 0;
Y = 0;
V0 = 50; // meters per second -- elevation
VX0 = V0 * cos(angle); // meters per second
VY0 = V0 * sin(angle); // meters per second
gameTime = 0;
// [self pauseSchedulerAndActions];
}
if (Y < 50)
{
[self unschedule:#selector(fire:)];
}
NSLog(#"ball (%lf,%lf), dt = %lf angle value %d", X, Y, dt,angleValue);
}
this code is working . by this code i can throw ball in projectile motion but i cant throw it where i want to. i cant throw wrt to given angle from start to end point.
i can throw it like red mark but i want to throw it blue mark with swipe . but its not throwing like i am swiping screen.

Answer 1

I am not certain on what math you are using to do this, I find your documentation a bit confusing.
Generally, for project tile motion this is what you need to do:
Find out what the take off angle is relative to the horizontal. Then depending on whatever initial velocity you want the object to have, use that and you trig equations to put your initial velocities into rectangular components.
For example:
If initial velocity was 10, the initial velocity in the y direction would be 10sin(angle), and in the x direction it would be 10cos(angle).
Then in to update the position of the sprite you should use kinematics equations: http://www.physicsclassroom.com/class/1dkin/u1l6c.cfm
First update velocities:
Velocity in the Y direction: V = v(initial) + gravity*(Delta-time)
Velocity in the X direction is constant unless you want to factor in some sort of resistance to make things a lot more complicated.
then position y = oldPositionY + velocity(in Y direction)*(Delta-time) + 1/2(gravity)(delta-time)^2.
and position x = oldPositionX + Xvelocity*delta-time
I have done some projectile motion stuff, and I have found you need to make gravity a large constant, something around 500 to make it look life-like. Let me know if this is confusing or you don't know how to implement it.
I would suggest that you take a look at the following tutorial: http://www.raywenderlich.com/4756/how-to-make-a-catapult-shooting-game-with-cocos2d-and-box2d-part-1.
It shows you how to use a physics engine, so you don't need to do much of the math. All the 'bullets' in the tutorial are also moving with projectile motion.

Answer 2

I'll add a bit to what was already said (which was good). Firstly, you should not be wasting time computing any angles. Stick with vectors for your velocity. In other words, get the initial velocity vector from the touch start and end location, and that will be your (v0x, v0y). For example:
CGPoint initialVelocity = ccpSub(touchPoint, startTouchPoint);
float v0x = initialVelocity.x;
float v0y = initialVelocity.y;
If you wish to assign a different magnitude to the initial velocity vector, simply normalize it and then multiply it by a new magnitude.
CGPoint unitVelocity = ccpNormalize(initialVelocity);
float magnitude = 200; // or whatever you want it to be
CGPoint velocity = ccpMult(unitVelocity, magnitude);
Anyway, with this velocity set properly you can then use it in your position calculations as before, but without the added complexity of calculating the angles.
-(void) fire:(ccTime)dt
{
.
.
gameTime += dt;
// if x(t) = x0 + v0x*t, then dx = v0x*dt
x += v0x*dt;
// if y(t) = y0 + v0y*t - 0.5t^2, then dy = v0y*dt - g*t*dt
y += (v0y * dt - g*gameTime*dt);
.
.
}
Also you should not set v0 = 50. Calculate the velocity from the vector as I suggested.
Something important to consider is that you are calculating what the movement should be in a physical world based upon units of meters. The screen is operating in points, not meters, so you will probably have to apply a scaling factor to the new position (x,y) to get the look that you are going for.
Edit: my bad, I had to revisit my math in the position calculation. My differentials was a bit rusty.