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:
y(0)=0.5 (centre of ball is 0.5m above ground level)
xdot(0)=Vcos(a) //a is the angle the ball is kicked at(unkown at this time)
and from newtons second law I have found
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
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!