It is commonly understood that a soccer goalie will be able
to kick the ball farther by doing a drop kick rather than a traditional punt. I
wanted to determine, by applying the physics we’ve learned in lecture, if this
is physically accurate. My question, then, became, does drop kicking truly allow
the ball to travel a greater horizontal distance? Below is a video tutorial on how to dropkick:

http://www.youtube.com/watch?v=Y9iBwrl5y8U

__Drop Kick__

**Assumptions**:

1. Height
of GK = 1.76 m (average of 3 GK’s on Colgate’s women’s team)

2. Mass
of ball = 0.45kg (FIFA Standard)

3. Velocity
of Kick = 30m/s

4. Time
of contact btw foot and ball = 0.05 s

5. Constant
force applied during kick

6. GK
either:

a. Drops
ball from mid-height; y

_{0}= 0.88m
b. Or
punts ball from mid-height

7. Height
ball reaches after bounce is negligible

8. Ignoring
air resistance

**To find v**

_{f}(when ball hits ground from drop):
V

_{f}^{2}= v_{0}^{2}+ 2a∆y à v_{f}= √( 2)(9.8m/s^{2})(0m – 0.88m)
V

_{f}= 4.15 m/s ** this will be our v_{0}when finding KE_{f}

**To find the force of the kick:**

F = ma =
m(v/t) = (0.45kg)(30m/s /0.05s)

F = 270 N

**To find KE**

_{f}:
∆KE = - ∆PE + W

_{NC}
KE

_{f}– 1/2mv_{0}^{2}= -∆PE + F_{foot}d(cosθ)
KE

_{f}= F_{foot}d(cosθ) + 1/2mv_{0}^{2}= (270N)(1.5m)(cos45°) + ½(0.45kg)(4.15m/s)^{2}
KE

_{f}= 290.3 J

**To find v**

_{o}:
KE = 1/2mv

^{2 }à v = √(2KE)/m = √[2(290.3 N)]/0.45kg
KE = 35.9 m/s

**To find range of drop kick:**

Vertical motion:

y = y

_{0}+v_{y0}t +1/2a_{y}t^{2}à 0 = 0 + v_{y0}t +1/2a_{y}t^{2}
t = (2v

_{y0})/g
Horizontal motion:

X = v

_{x0}t = v_{x0}[(2v_{y0})/g] = (2v_{x0}v_{yo}) / g = [(2)(25.4m/s)(25.4m/s)] / 9.8 m/s^{2}

__X = 122.5 m__

__Punt__

**To find v**

_{0}:
KE

_{f }= F_{foot}d(cosθ)
d = vt = (30 m/s)(0.05s) = 1.5m over which F

_{foot}was applied
Assuming, θ= 45°

1/2mv

_{0}^{2}= F_{foot}d(cosθ) à v_{0}= √(2KE)/m = √[2(286.4 J)] / 0.45 kg
v

_{0}= 35.7 m/s**To find range of punt:**

Since the vertical point of origin is above the point where the ball hits the ground, we need to be careful when defining our vertical values:

Vertical Motion:

y = y

_{0 }+ v_{y0}t – 1/2gt^{2}à 0 = -4.9t^{2}+ 25.2t +0.88
t = 5.2 s

Horizontal Motion:

X = v

_{x0}t = (25.2 m/s)(5.2s)

__X = 131.0 m__

__Conclusion__
According
to my calculations, the traditional punting technique actually allows the ball
to travel a greater horizontal distance than does the drop kicking technique.
This may be the result of all of the preliminary assumptions made, but regardless,
it may be wise for goalkeepers to focus on improving other parts of their game!

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