Test for PSE 5E Problem 4.11

Tests/Tests.cs

@@ -594,6 +594,142 @@ static void Main(string[] args)
 
             #endregion
 
+            #region PSE 5E PROBLEM 4.11
+
+            {
+                // One strategy in a snowball fight is to throw a first snowball at a 
+                // high angle over level ground. While your opponent is watching the
+                // first one, you throw a second one at a low angle and timed to arrive 
+                // at your opponent before or at the same time as the first one. Assume 
+                // both snowballs are thrown with a speed of 25.0 m/s. The first one is 
+                // thrown at an angle of 70.0° with respect to the horizontal.
+                // 
+                // (a) At what angle should the second (low-angle) snowball be thrown 
+                // if it is to land at the same point as the first?
+                //
+                // (b) How many seconds later should the second snowball be thrown if it 
+                // is to land at the same time as the first?
+
+                var xA = new Symbol("xA");      // position.x at point A
+                var yA = new Symbol("yA");      // position.y at point A
+                var th1A = new Symbol("th1A");  // angle of snowball 1 at point A
+                var vA = new Symbol("vA");      // velocity at point A
+
+                var g = new Symbol("g");        // magnitude of gravity
+                var _g = new Point(0, -g);      // gravity vector
+
+                //Func<MathObject, MathObject> numeric = obj =>
+                //    obj
+                //        .Substitute(xA, 0)
+                //        .Substitute(xB, 1.4)
+                //        .Substitute(yA, 0.86)
+                //        .Substitute(g, 9.8)
+                //        .Substitute(Trig.Pi, 3.14159);
+
+                var obj1A = new Obj()           // snowball 1 at initial point
+                {
+                    position = new Point(xA, yA),
+                    velocity = Point.FromAngle(th1A, vA),
+                    acceleration = _g,
+                    time = 0
+                };
+
+                var obj1B = new Obj()            // snowball 1 at final point
+                {
+                    position = new Point(null, 0),
+                    velocity = new Point(obj1A.velocity.x, null),
+                    acceleration = _g
+                };
+
+                var time1B = Calc.Time(obj1A, obj1B, 1);
+
+                obj1B = obj1A.AtTime(time1B);
+
+                var obj2A = new Obj()           // snowball 2 at initial point
+                {
+                    position = obj1A.position,
+                    speed = vA,
+                    acceleration = _g
+                };
+
+                var obj2B = new Obj()           // snowball 2 at final point
+                {
+                    position = obj1B.position,
+                    acceleration = _g
+                };
+
+                //Calc.InitialAngle(obj2A, obj2B, 1, 0)
+                //    .Substitute(yA, 0)
+                //    .Substitute(th1A, (70).ToRadians())
+                //    .Substitute(vA, 25)
+                //    .Substitute(Trig.Pi, 3.14159)
+                //    .Substitute(g, 9.8)
+                //    .ToDegrees()
+                //    .Substitute(Trig.Pi, 3.14159)
+                //    .Disp();
+
+                var th2 = Calc.InitialAngle(obj2A, obj2B, 1, 0);
+
+                //("At what angle should the second (low-angle) snowball " +
+                //"be thrown if it is to land at the same point as the first?").Disp();
+
+                //"".Disp();
+
+                //"symbolic:".Disp();
+
+                //th2.Disp(); "".Disp();
+
+                //"numeric:".Disp();
+
+                AssertEqual(
+                    th2
+                        .ToDegrees()
+                        .Substitute(yA, 0)
+                        .Substitute(th1A, (70).ToRadians())
+                        .Substitute(vA, 25)
+                        .Substitute(g, 9.8)
+                        .Substitute(Trig.Pi, Math.PI),
+                    20.000000000000007);
+
+                //"".Disp();
+
+                obj2A.velocity = Point.FromAngle(th2, vA);
+
+                var time2B = Calc.Time(obj2A, obj2B, 1);
+
+                //("How many seconds later should the second snowball be thrown if it " +
+                //"is to land at the same time as the first?").Disp();
+
+                //"".Disp();
+
+                //"symbolic:".Disp();
+
+                //(time1B - time2B).Disp(); "".Disp();
+
+                //"numeric:".Disp();
+
+                //(time1B - time2B)
+                //    .Substitute(yA, 0)
+                //    .Substitute(th1A, (70).ToRadians())
+                //    .Substitute(vA, 25)
+                //    .Substitute(Trig.Pi, 3.14159)
+                //    .Substitute(g, 9.8)
+                //    .Disp();
+
+                AssertEqual(
+                    (time1B - time2B)
+                        .Substitute(yA, 0)
+                        .Substitute(th1A, (70).ToRadians())
+                        .Substitute(vA, 25)
+                        .Substitute(Trig.Pi, 3.14159)
+                        .Substitute(g, 9.8),
+                    3.0493426265020469);
+
+                //Console.ReadLine();
+            }
+
+            #endregion
+
             Console.WriteLine("Testing complete");
 
             Console.ReadLine();