# addition and subtraction of vectors

In a soccer match, the goal keeper stands on the midpoint of her goal line. she kicks the ball 25m at an angle of 35deg to the goal line. her teammate takes the pass and kicks it 40m farther, parallel to the sideline.

The resultant vector is 62.2m

if the field is 110m long, how far must the next player kick the ball to take a good shot at the center of the goal, and in approximately which direction?

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1. I see it as

(25cos35°,25sin35°) + (0,40) + (acosØ,asinØ) = (0,110)
where a is the magnitude of the last kick and Ø is its direction.

simplifying we get
acosØ = -25cos35° = -20.4788 and
asinØ = 110 - 25sin35° - 40 = 55.66
so we can do
asinØ/acosØ = 55.66/-20.4788
tanØ = -2.71796
Ø = 110.1997° (I picked the quadrant II angle from my diagram)
then asin110.1997° = 55.662
a = 59.3

I did not get your answer, but I am sure of my method, perhaps I made a calculation error.
but
(25cos35,25sin35) + (0,40) + (59.3cos110.2,59.3sin110.2) = (0,110)

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