Given :
A kayak on a lake is moving at a constant speed of 4.1 m/s in a direction 41.6° north of west.
To Find :
After 10 min :
(a) how far west the kayak has traveled km.
(b) how far north the kayak has traveled km.
Solution :
a) Time taken in seconds :
[tex]t=10\times 60 \ s = 600\ s[/tex] .
Distance travelled in 600 s is :
[tex]D=s\times t\\\\D=4.1\times 600\ m\\\\D=2460\ m[/tex]
Distance in km is :
[tex]D=\dfrac{2460}{1000}=2.46\ km[/tex]
b) Now , distance from the north is given by :
[tex]d=D\times sin\ 41.6^o\\\\d=2.46 \times sin\ 41.6^o\\\\d=1.63\ km[/tex]
Hence , this is the required solution .
