Suggestions for Soccer Goalkeepers

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; y₀ = 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_f² = v₀² + 2a∆y à v_f = √( 2)(9.8m/s²)(0m – 0.88m)

V_f = 4.15 m/s ** this will be our v₀ 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 – 1/2mv₀² = -∆PE + F_footd(cosθ)

KE_f = F_footd(cosθ) + 1/2mv₀² = (270N)(1.5m)(cos45°) + ½(0.45kg)(4.15m/s)²

KE_f = 290.3 J

To find v_o:

KE = 1/2mv² à v = √(2KE)/m = √[2(290.3 N)]/0.45kg

KE = 35.9 m/s

To find range of drop kick:

Vertical motion:

y = y₀ +v_y0t +1/2a_yt² à 0 = 0 + v_y0t +1/2a_yt²

t = (2v_y0)/g

Horizontal motion:

X = v_x0t = v_x0[(2v_y0)/g] = (2v_x0v_yo) / g = [(2)(25.4m/s)(25.4m/s)] / 9.8 m/s²

X = 122.5 m

Punt

To find v₀:

KE_f  = F_footd(cosθ)

d = vt = (30 m/s)(0.05s) = 1.5m over which F_foot was applied

Assuming, θ= 45°

1/2mv₀² = F_footd(cosθ) à v₀ = √(2KE)/m = √[2(286.4 J)] / 0.45 kg

v₀ = 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 = y₀ + v_y0t – 1/2gt² à 0 = -4.9t² + 25.2t +0.88

t = 5.2 s

Horizontal Motion:

X = v_x0t = (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!