A drone is heading due east at 20 mih relative to the air Th

A drone is heading due east at 20 mi/h relative to the air. The wind is blowing due north at 10 mi/h. (a) Express the velocity of the drone relative to the air, as a vector in component form. (b) Express the velocity of the wind, as a vector in component form. (c) Find the true velocity of the drone, as a vector in component form. (d) Find the true speed and direction of the drone. Round to one decimal.

Solution

a)

velocity of drone relative to air ,v_da= 20 i

b)

velocity of wind ,v_ag= 10 j

c)

true velocity of drone,v_dg=v_da+v_ag

true velocity of drone,v_dg=20 i+10 j

d)

true speed =|v_dg|

true speed =[20²+10²]

true speed =22.36068 mi/hr

true speed =22.4 mi/hr

direction =N(90^o-tan^-1(10_/20))E

direction =N(90^o-26.565^o)E

direction =N63.4^oE