Why T Does T Melon T Score T So T Well T ? T
US Dream Team in the Olympic games - Barcelona 92
Melon ( the Mailman ) is on the foul line .
Why does he have such an high percentage scores ?
Click on the image below to see the video
(By the way , in the image there are 2 very famous NBA stars (beside Melon).
WHO are they ?
(The answer is on the bottom of the page ! )
The VIOLET line shows the trace of the ball from Melon hand to the ring.
The YELLOW vertical lines mark the ball locations in the succesive frames.
The TIME distance between 2 succesive frames is 40 milisecond (0.040 second).
(It was samples from the European PAL standard with 25 frames per second )
In the following computations: ( See the marked notations on the above image)
g --> The gravitation accelaration is 9.8 m/sec2
V0 --> The initial velocity of the ball after leaving Melon's hand.
a --> The initial angel of the ball after leaving Melon's hand.
tp --> The time between the ball leaving Melon's hand up to its highest point.
It's easy to compute it by counting the number of frames :
tp = 0.58 second ( 14.5 frames * 0.040 sec/frame )
It's known from mechanics that : . . . V0 * SIN(a) = g * tp
By substituting the known value for g (9.8) and tp (0.58) we get :
(1) . . . V0 * SIN(a) = 9.8*0.58 = 5.684 m/sec
h --> The vertical height between the final point (entering the ring) and the point of the ball leaving Melon's hand.
tf --> The ball time between leaving Melon's hand up to its final point - the ring.
It's easy to compute it by counting the number of frames :
(2) . . . tf = 0.96 second ( 24 frames * 0.040 sec/frame )
It's known from mechanics that : . . . h = V0*SIN(a)*tf - (g/2)*tf2
By substituting the known value from (1) for V0 * SIN(a) and tf (0.96) we get :
(3) . . . h = 5.684*0.96 - (9.8/2)*0.962 = 0.94 m
L1 --> The horizontal distance between the foul line and the ring center.
By measuring on the image above (with ruler) the lengths of h and L1 , we get :
(4) . . . h/L1 = 2/9 ---------> L1 = (9/2)*h
By substituting in (4) h=0.94 (from (3)) , we get :
(5) . . . L1 = (9/2)*0.94 = 4.23 m .
(nicely matched with the official value 4.225 m )
It's known from mechanics that : . . . L1 = V0*COS(a)*tf
By substituting tf = 0.96 from (2) we get :
(6) . . . V0*COS(a) = 4.23/0.96 = 4.406 m/sec
Now we have two trigonometric equations (1) and (6) with two unkown parameters :
the angel a and the initial velocity V0
Dividing (1) by (6) gives : . . .(7) . . . TAN(a) = 5.684/4.406 = 1.29
Computing angel a from (7) gives . . .(8) . . . a = 52.2 0
By substituting angle a=52.2 into (1) or (6) we get : . . .(9) . . .V0 = 7.2 m/sec
Thus, we know that :
V0 --> The initial velocity of the ball after leaving Melon's hand is 7.2 m/sec.
a --> The initial angle of the ball after leaving Melon's hand is 52.2 degrees
And now back to the main question :
Why does Melon score so well from the foul line ?
The answer is that he is VERY CLOSE to the OPTIMAL ANGLE of about 51 degrees !
The meaning of OPTIMAL ANGLE is the angle in which a certain shift in the angle causes the smallest horizontal shift of the ball when reaching the ring
He is just 1 degree beyond the optimal angel ( 52.2 degree instead of 51 degree )
Accuracy of 1 deg means accuracy of the shift of the fingers by about 0.5 cm !
( Assuming hand palm of 30 cm , 30*tan(1) = 0.5 cm )
Melon's shift of 1 degree from the optimal angle caused shift of about 1 cm aside of the ball on reaching the ring
( The ball's diameter is about 24 cm and the ring diameter is about 45 cm , so there is a spare of 10 cm on each side of the ball )
For a detailed explanation about the OPTIMAL ANGLE and how it is computed ,
choose BASKETBALL and CALCULUS !
See also on BASKETBALL and TRIGONOMETRY :
Why did Melon miss the foul shot ? !
(The 2 very famous NBA stars (beside Melon) are: Bird (white shirt,face) and Uing (white shirt,back).
