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A soccer player takes a cor- ner kick, lofting a stationary ball 35.0° above the horizon at 22.5 m/s. If the soccer ball has a mass of 0.425 kg and the player’s foot is in contact with it for 5.00 x 10-2 s, find (a) the x - and y - components of the soc- cer ball’s change in momentum and (b) the magnitude of the average force exerted by the player’s foot on the ball.

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Answer:

(a)

x=7.83 Kgm/s

y=5.48 Kgm/s

(b)

191.25 N

Explanation:

(a)

Change in momentum in x direction

[tex]P_{x}=mvcos\theta[/tex] where m is mass and v is the velocity and [tex]\theta[/tex] is the angle of kick  

Substituting m=0.425 Kg, v=22.5m/s and [tex]\theta=35^{o}[/tex]

[tex]P_{x}=0.425*22.5*cos 35= 7.833141424[/tex]

[tex]P_{x}=7.83 Kgm/s[/tex]

Change in momentum in y direction

[tex]P_{y}=mvsin\theta[/tex]

[tex]P_{y}=0.425*22.5*sin 35= 5.484824673[/tex]

[tex]P_{y}=5.48 Kgm/s[/tex]

(b)

Force exerted by the player

F=mv/t where t is time

Substituting [tex]t=5*10^{-2} s[/tex]

F=(0.425*22.5)/0.05= 191.25 N

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