- #1

ekpm

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- Homework Statement
- Two soccer players, Mia and Alice, are running as Alice passes the ball to Mia. Mia is running due north with a speed of 6.00 m/s. The velocity of the ball relative to Mia is 5.00 m/s in a direction 30.0 degrees east of south. What are the magnitude and direction of the velocity of the ball relative to the ground.

- Relevant Equations
- V(B/G) = V(B/M) + V(M/G)

For some reason I'm having trouble understanding relative velocity problems. I know how to solve this, but I keep guessing at random methods until my answer matches the solution in the textbook.

I solved it correctly by breaking the velocity of the ball into x- and y- components, then solved for the components of V(B/G) (2.50 m/s and -4.33 m/s) and using the Pythagorean theorem to get 3.01 m/s and the angle arctan(1.67/2.50) = 33.7 degrees N of E.

But that's not the answer I got the first time when I drew a diagram. Why is the answer not V(B/G) = V(B/M) + V(M/G) = (-5.00 + 6.00) = 1.00 m/s in 30 degrees east of south (the same direction as the velocity of the ball relative to Mia.

I'm having trouble wrapping my head around what is going on. Alice has to be ahead of Mia kicking the ball back to Mia in order for it to travel east of south (Quadrant IV) in respect to Mia running north. But somehow the solution has the ball traveling North? This would mean the ball is traveling in two different directions at the same time because Mia is traveling North.

I solved it correctly by breaking the velocity of the ball into x- and y- components, then solved for the components of V(B/G) (2.50 m/s and -4.33 m/s) and using the Pythagorean theorem to get 3.01 m/s and the angle arctan(1.67/2.50) = 33.7 degrees N of E.

But that's not the answer I got the first time when I drew a diagram. Why is the answer not V(B/G) = V(B/M) + V(M/G) = (-5.00 + 6.00) = 1.00 m/s in 30 degrees east of south (the same direction as the velocity of the ball relative to Mia.

I'm having trouble wrapping my head around what is going on. Alice has to be ahead of Mia kicking the ball back to Mia in order for it to travel east of south (Quadrant IV) in respect to Mia running north. But somehow the solution has the ball traveling North? This would mean the ball is traveling in two different directions at the same time because Mia is traveling North.