Any mathematical wizards out there?
If a player is running forward at say 20 mph, and releases the ball exactly lateral , then how further forward will the ball have travelled if it is caught 5m, 10m 15m or 20m from where it left the passers hands?
Ive just watched Burrells pass v Sarries & this set me thinking of the optimum, from which decisions could be benchmarked.
Insufficient data. The result will depend on how fast the pass is thrown, among other things;
The simple solution is a vector diagram. In simple terms (discounting gravity which causes the ball to fly in a parabolic arc, and air resistance which will lead to deceleration)
The forward vector is momentum/forward velocity - we'll call that V[SUB]m[/SUB]
The lateral vector is the speed the pass is thrown - we'll call that V[sub]l[/sub]
The result is the distance and the direction the ball travels - we'll call that D[sub]f[/sub]
If the player is running forward at the same speed he throws the lateral pass, then V[SUB]l[/SUB] = V[sub]m[/sub]. The ball travels forward at an angle of 45°, (the black arrow)
If the player is running forward at half the speed he throws the lateral pass, then V[SUB]l[/SUB] = 2 x V[sub]m[/sub]. The ball travels forward at an angle of 26°, (the red arrow)
If the player is running forward at a quarter of the speed he throws the lateral pass, then V[SUB]l[/SUB] = 4 x V[sub]m[/sub]. The ball travels forward at an angle of 14°, (the green arrow)
It is easy to work out that so long as the player is running forwards, no matter how fast the ball is thrown, in a lateral pass, it WILL always travel forwards. Any value of V[SUB]m[/SUB] greater than zero will result in a forward angle of greater than zero. Its why the momentum rule makes sense and the classic interpretation doesn't.
Changes in the direction of V[SUB]m[/SUB] will alter the result, as will air resistance,