Please help us to solve this question by using Java codes and to plot graph of it!!! Solution package examples; import java.io.*; import java.util.*; import sos.db.*; public boolean checkBounds() { if(bX1 == bX2 || bY1 == bY2) { return false; } double xa = 0D; double ya = 0D; int a = 0; boolean hC = false; double xn = 0D; double yn = 0D; for(double[] vertex : this.getShape().getVerticies()) { if(vertex[0] >= bX2) { xa += vertex[0]; ya += vertex[1]; a++; hC = true; xn -= 1D; } if(vertex[0] <= bX1) { xa += vertex[0]; ya += vertex[1]; a++; hC = true; xn += 1D; } if(vertex[1] >= bY2) { xa += vertex[0]; ya += vertex[1]; a++; hC = true; yn -= 1D; } if(vertex[1] <= bY1) { xa += vertex[0]; ya += vertex[1]; a++; hC = true; yn += 1D; } } if(hC) { Vec2 n = new Vec2(xn, yn).uscale(); Vec2 cp = new Vec2(xa / a, ya / a); Vec2 rap = cp.sub(getShape().getCM()); Vec2 va = getVelocityAt(rap); Vec2 rva = va; Vec2 rvb = Vec2.ZERO_VEC.sub(va); double pj = -(1D + getElasticity()) * rva.dot(n); double j = pj / (1 / getShape().getMass() + Math.pow(rap.cross(n), 2D) / getShape().getMass()); applyForce(new AppliedForce(n.scale(j), rap, getShape().getMass())); } return hC; } public void applyForce(AppliedForce... f) { for(AppliedForce vec : f) { Vec2 a = vec.getForce().divide(getShape().getMass()); applyLinearAcceleration(a); double aa = a.relativeCosine(getShape().getTangent(vec.getOffsetCM())) * a.getMagnitude() / getShape().getMass(); applyAngularAcceleration(aa); } } .

1. Please help us to solve this question by using Java codes and to plot graph of it!!!
Solution
package examples;
import java.io.*;
import java.util.*;
import sos.db.*;
public boolean checkBounds() {
if(bX1 == bX2 || bY1 == bY2) {
return false;
}
double xa = 0D;
double ya = 0D;
int a = 0;
boolean hC = false;
double xn = 0D;
double yn = 0D;
for(double[] vertex : this.getShape().getVerticies()) {
if(vertex[0] >= bX2) {
xa += vertex[0];
ya += vertex[1];
a++;
hC = true;
xn -= 1D;
}
if(vertex[0] <= bX1) {
xa += vertex[0];
ya += vertex[1];
a++;
hC = true;
xn += 1D;
}
if(vertex[1] >= bY2) {

2. xa += vertex[0];
ya += vertex[1];
a++;
hC = true;
yn -= 1D;
}
if(vertex[1] <= bY1) {
xa += vertex[0];
ya += vertex[1];
a++;
hC = true;
yn += 1D;
}
}
if(hC) {
Vec2 n = new Vec2(xn, yn).uscale();
Vec2 cp = new Vec2(xa / a, ya / a);
Vec2 rap = cp.sub(getShape().getCM());
Vec2 va = getVelocityAt(rap);
Vec2 rva = va;
Vec2 rvb = Vec2.ZERO_VEC.sub(va);
double pj = -(1D + getElasticity()) * rva.dot(n);
double j = pj / (1 / getShape().getMass() + Math.pow(rap.cross(n), 2D) / getShape().getMass());
applyForce(new AppliedForce(n.scale(j), rap, getShape().getMass()));
}
return hC;
}
public void applyForce(AppliedForce... f) {
for(AppliedForce vec : f) {
Vec2 a = vec.getForce().divide(getShape().getMass());
applyLinearAcceleration(a);
double aa = a.relativeCosine(getShape().getTangent(vec.getOffsetCM())) * a.getMagnitude() /
getShape().getMass();
applyAngularAcceleration(aa);
}
}