# Developing a Euler method from the motion of a ball to find out where it lands

• Oct 19th 2012, 03:03 PM
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Developing a Euler method from the motion of a ball to find out where it lands
A ball is kicked at a 5m vertical wall at a distance of 20m away. The ball has a speed Vm/s and an initial angle of motion a. When the ball strikes the wall it bounces back with coefficient of restitution b, eventually returning to the level ground.

The forces acting on the ball are gravity and a wind that acts at right angles to the initial motion of the ball, which generates a force of WN

The ball has diameter of 1 metre and weighs 0.5 kg.

I am required to develop the ordinary differential equations dictating the motion of the ball and reduce these to a system of first order equations. Then create a Euler time stepping algorithm to approximate the ODE's and determine when the ball hits the wall.

I have started the problem as follows -

I have developed the following initial conditions:
x(0)=0
y(0)=0.5 (centre of ball is 0.5m above ground level)
z(0)=0

xdot(0)=Vcos(a) //a is the angle the ball is kicked at(unkown at this time)
ydot(0)=Vsin(a)
zdot(0)=0

and from newtons second law I have found

xdoubledot=0
ydoubledot=-g
zdoubledot=W/m //W is the wind force, m the mass of the ball

I have integrated these twice and applied the intial conditions to find

xdot(t)=Vcos(a)
ydot(t)=Vsin(a)
zdot(t)=0

x(t)=Vcos(a)t
y(t)= -0.5gt squared + Vsin(a)t +0.5
z(t)= ((W/m)/2)t squared

At this point I am required to create a Euler method to compute the location where the ball strikes the ground but really have no clue what to do. Any help or links would be much appreciated!
• Oct 19th 2012, 03:06 PM
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Re: Developing a Euler method from the motion of a ball to find out where it lands
After studying the tutorial thread "Part I: First Order Equations and Homogeneous Second Order Equations" I have a feeling I may have started solving the problem incorrectly as I do not have a function to represent the motion? Is it possible to achieve such a function with the variables that are provided?