How Do You Calculate the Velocity of a Soccer Ball Relative to the Ground?

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To calculate the velocity of the soccer ball relative to the ground, first determine the components of both Mia's velocity and the ball's velocity relative to her. For the initial scenario, Mia's northward velocity is 5.80 m/s, while the ball's velocity is 5.90 m/s at 30 degrees east of south, requiring vector addition to find the resultant velocity. In the second scenario, Mia's speed is 6 m/s north, and the ball moves 7 m/s directly south, again necessitating vector calculations to ascertain the ball's ground velocity. Diagrams can aid in visualizing the problem, and applying the Pythagorean theorem and trigonometric functions will simplify the calculations. Understanding these principles is essential for accurately determining the ball's velocity relative to the ground.
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Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 5.80 . The velocity of the ball relative to Mia is 5.90m/s in a direction 30.0 degrees east of south.

What is the magnitude of the velocity of the ball relative to the ground?

What is the direction of the velocity of the ball relative to the ground?

How should I start this other then making a diagram haha. Which formulas.
 
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Perhaps consider how you would solve this much simpler problem first...

Mia is running due north with a speed of 6m/s. The velocity of the ball relative to Mia is 7m/s in a direction due south. What is the magnitude of the velocity of the ball relative to the ground?
 

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