a bird has a flight speed in still air of 9.2ms^-1. it is pointed in the direction S41(degree)E but flies in the wind of speed 12.3ms^-1 from the direction N54E . Take i to be 1m s^-1 due east and j to b 1ms^-1 due north. Also take

Vb to be the velocity of the bird in still air,
Vw to be velocity of the wind
V to be the resultant velocity of the bird


A) express each of the vectors for brid(Vb) and wind (Vw) in component form, giving the components to four decimal places.

B) Hence show that the resultant velocity V of bird is given in component form approx by

V= -3.9152i - 14.1731j

C) by putting V into geometric form find the overall IVI of the bird and its direction of travel as bearings- with angle in degree to one decimal point.

D) the bird begins its flight from a point on the north bank of a river that flows due east and is 180 meters wide. how long does it take the bird to cross the river, and what distance has it travelled in that time? give your answer in seconds and meters, to three significant figures

I puzzled a minute over "brid"!

The bird is flying at 41 degrees S of D so 41 degrees below the i axis. Set this up as a right triangle with hypotenuse of length 9.2 and angle 41 degrees. The leg along the x-axis is 9.2 cos(41) and along the y-axis is -9.2 sin(41). The components are 9.2 cos(41)i -9.2 sin(41)j.

The wind is blowing "N 53 degrees E" or 54 degrees above the x-axis with speed 12.3. Its components are 12.3 cos(54)i+ 12.3 sin(54)j.

B) Hence show that the resultant velocity V of bird is given in component form approx by

V= -3.9152i - 14.1731j[/quote]
Add the components above.

[qupte]C) by putting V into geometric form find the overall IVI of the bird and its direction of travel as bearings- with angle in degree to one decimal point.[/quote]
Assuming the V above is correct, you can find the "overall |V|" by using the Pythagorean theorem: and the angle by using the fact that the tangent of the angle is "opposite over near" or "y over x": .

The vector flown after t seconds is -3.9152ti- 14.1712tj. Since crossing the river requires that southward motion be 180, solve -14.1712t= 180.