Question

Grade 12 vectors: velocity?
Mary leaves a dock, paddling her canoe at 3 m/s. She heads downstream at an angle of 30 degrees to the current, which is flowing at 4 m/s. How far downstream does Mary travel in 10s?

Answer: about 66m

How do you solve this? I don't know how to draw the diagram...

Answer 1

we know magnitude and direction of both vectors right?

Answer 2

hey amistre got ya another one above this q when ur done mate

Answer 3

we also have a scalar of 10

Answer 4

scale the vectors then add them

30 degrees = has a unit vector of <sqrt(x),1>

so at 3<sqrt(3),1> = <3sqrt(3),3>

10<3sqrt(3),3> + 10<0,4> =

<30sqrt(3),30>
< 0 ,40>
---------------
<30sqrt(3), 70> right?

Answer 5

the magnitude of this vector should be the distance traveled

Answer 6

sqrt(70^2 + 30sqrt(3)^2)

sqrt(4900 + 900(3))

sqrt(7600) right?

Answer 7

87.1779... to find the distance travled downstream tho, we take this distance and multiply it by the cos(30) to get a vector projection

Answer 8

what i come up with is: 75.49

but then I could be wrong

Answer 9

did you typo the question?

Answer 10

No, there's no typo. But thanks amistre! :)

Answer 11

ok i have a Q, how far did she paddle on the horizon before she went to the 30 degree angels downstream, some data is missing i believe