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Throwing with the wind, a quarterback passes a football 140 ft in 2 s. against the wind, the same pass would have traveled 80 ft in 2 s. find the rate of the pass and the rate of the wind.

Respuesta :

When we throw the ball along the direction of the wind then the net speed of the ball is sum of speed of ball and speed of wind.

[tex]v = v_{ball} + v_{wind}[/tex]

[tex]\frac{140}{2} = 70 ft/s = v_{ball} + v_{wind}[/tex]

Now when wind is blowing opposite to the direction of the ball then net speed is subtraction of ball speed and wind speed

[tex]v = v_{ball} - v_{wind}[/tex]

[tex]\frac{80}{2} = 40 ft/s = v_{ball} - v_{wind}[/tex]

Now if we subtract above two equations

[tex]70 - 40 = 2*v_{wind}[/tex]

[tex]v_{wind} = 15 ft/s[/tex]

so wind speed will be 15 ft/s

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