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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A soccer player takes a corner 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 × 10−2 s, find (a) the x- and y - components of the soccer ball’s change in momentum and (b) the magnitude of the average force exerted by the player’s foot on the ball.

(a)

To determine
The change in momentum of the soccer ball at the  x and y component .

Explanation

Given info: mass is 0.425kg , velocity is 22.5m/s , angle θ is 35.0° .

Explanation:

Formula to calculate change in momentum on the x – component,

ΔPx=(Pf,xPi,x)cosθ

  • ΔPx is the change in momentum on the x – component,
  • Pf,x is the change in final momentum,
  • Pi,x is the change in initial momentum,
  • θ is the angle the ball is kicked with respect to ground,

Since, initially the soccer ball is at rest, so Pi,x is Zero.

Use mvx for Pf,x and 0 for Pi,x in the above equation to find the expression ΔPx .

ΔPx=mvxcosθ

  • m is the mass of the soccer ball,
  • vx is the velocity at the x – component,

Substitute 0.425kg for m, 35.0° for θ and 22.5m/s for vx to find ΔPx .

ΔPx=(0.425kg)(22.5m/s)cos35.0°=(9.5625kgm/s)(0.819)=7.83kgm/s

Thus, the change in momentum of the soccer ball at the x component is 7

(b)

To determine
The magnitude of the average force exerted by the player’s foot on the ball.

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