Vectors. Riding a bike with velocity (4i − 8j) km/h the wind seems to have velocity (−i − 2j) km/h. What is...?
To a person riding a bike with velocity (4 i − 8 j) km/h the wind seems to have velocity (− i − 2 j) km/h.
1) State the true velocity of the wind in i, j vector form
2) What is the speed of the wind?
3) Taking i as due East, what is the direction of the wind (in standard bearing notation) to the nearest degree?
How do you tackle this?
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Let the wind's true velocity be ai+bj
The velocity felt Blythe rider would be
ai+bj - (4i-8j) = (a-4)i + (b+8)j
Thus, -1i-2j = (a-4)i + (b+8)j
a=3, b=-10
The wind' velocity is 3i -10j
The speed is sqrt(3^2+ (-10)^2) = sqrt(109)
The angle is arctan(-10/3) = -73.3 or 286.7 degree