Posted by **bobjahng** on Tuesday, November 2, 2010 at 7:33pm.

In a World Cup soccer match, Juan is running due north toward the goal with a speed of 7.80 m/s relative to the ground. A teammate passes the ball to him. The ball has a speed of 13.6 m/s and is moving in a direction of 32.5 degrees east of north, relative to the ground.

a)What is the magnitude of the ball's velocity relative to Juan?

b)What is the direction of the ball's velocity relative to Juan?

How do you start this off? I found the y component and subtracted it to find the answer for the first part, but it says that my answer is wrong.

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**bobpursley**, Tuesday, November 2, 2010 at 7:43pm
a) ball relativeground=Juansspeed+ball relative to Juan

13.6Cos32.5N + 13.6Sin32.5E =7.8N+ballrelative to Juan

ball relative to Juan= (13.6Cos32.5-7.8)N+13.6Sin32.5E

so figure out the N component, then magnitude= sqrt (Ncomp^2+Ecomp^2)

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**bobjahng**, Tuesday, November 2, 2010 at 7:55pm
i got the right answer for part a (8.18)

now how do i do part b?

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**bobpursley**, Tuesday, November 2, 2010 at 8:27pm
you have the vector:

Ncomp, E component

relative to Juan, going N, so it is E of him by theta, where tantheta=Ecomp/Ncomp

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**billy**, Wednesday, November 3, 2010 at 3:13pm
i cant get part b!!!!!!! im completely lost >.<

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**Juan**, Friday, February 17, 2012 at 4:14am
Hi Chris

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**El Piton**, Friday, February 17, 2012 at 4:15am
On that Kobe System.

Or Linsanity

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**Annie**, Tuesday, September 25, 2012 at 8:46pm
Make sure you're putting the parenthesis in the correct place. Such as for part A, the formulas should be:

a) (ball relative ground) = (Juan's speed)+ (ball relative to Juan)

(13.6Cos(32.5))N + (13.6Sin(32.5))E =(7.8)N+(ball relative to Juan)

ball relative to Juan= (13.6(Cos(32.5))-7.8)N+(13.6Sin(32.5))E

so figure out the N component, then magnitude= sqrt (Ncomp^2+Ecomp^2)

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