Hi

Can someone verify these answers are correct (or at least say where I went wrong)? Thanks

$\displaystyle v_{b}$ = velocity of bee in still air (speed = 6.7ms^-1; directon = N25 degrees E)

$\displaystyle v_{b}$ = 6.7cos(90-25)i + 6.7sin(90-25)j = 2.8315i + 6.0723j

$\displaystyle v_{w}$ = velocity of the wind (speed = 10.3ms^-1; direction = S54 degrees E)

$\displaystyle v_{w}$ = 10.3cos(90+54)i + 10.3sin(90+54)j = -8.3329i + 6.0542j

v = resultant velocity of bee

$\displaystyle v_{b} + v_{w}$ = (2.8315i + -8.3329i) + (6.0723j + 6.0542j)

$\displaystyle v_{b} + v_{w} = v$ = -5.5013i + 12.1265j

Convert v into geometric form and find the overall speed of the bee and it's direction of travel as a bearing:

$\displaystyle \abs{v}$ = sqrt((-5.5013)^2 + 12.1265^2) = sqrt(177.3155) = 13.3 ms^-1

Angle = arctan(12.1265/-5.5013) = arctan(2.2043) = 1.1449 = 65.6 degrees

Second quadrant = 180 - 65.5979 = 114.4 degrees

bearing = N(114.4-90) degrees W = N24.4 degrees W

Find the time taken by the bee to travel 1km:

Time to travel 1km = 1000 / 13.3160 = 82.5 seconds

Find the distance west it travels in that time

Distance west = 82.4644 * -8.3329 = 687 metres