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A quarterback throws a football with a velocity of 41 mph and a direction of 168°. The wind on the field is 11 mph with a direction of 339°. What are the true speed and direction of the football? Round the speed to the thousandths place and the direction to the nearest degree.

29.725; 171°
30.185; 171°
29.725; 9°
30.185; 9°

Respuesta :

onyebuchinnaji

The true speed and direction of the football thrown by the  quarterback is 30.185 mph and 9⁰ respectively.

Relative velocity of the football

The true speed and direction of the football is determined by applying the concept of relative velocity.

Vr/w = Vb - Vw

where;

  • Vr/w is the velocity of the football with respect to the wind
  • Vb is the velocity of the football
  • Vw is the velocity of the wind

Vr/w = 41 mph - 11 mph = 30 mph

The direction speed can be determined by sketching a triangle

Direction of the speed, θ = (360 - 339) - (180 - 168)

                                       θ = 21 - 12 = 9⁰

Resultant speed;

R² = 41² + 11² - 2(41 x 11 x cos9)

R² = 911.105

R = √911.105

R = 30.185 mph

Thus, the true speed and direction of the football thrown by the  quarterback is 30.185 mph and 9⁰ respectively.

Learn more about relative velocity here: https://brainly.com/question/17228388

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