A unman airplane (drone) flies at a constant speed of 375 km/h at a bearing of south 83 degrees due east, with a 42 km/h crosswind of east 20 degrees north. What is the actual speed and direction of the drone?

Guest Nov 25, 2014

#1**+5 **

I'll do this one with vectors

S83°E = 353°

E20°N = 20°

So, the first vector is <375cos353 , 375sin353 > ....and the second vector is <42cos20, 42sin20>

So the x component of the resultant vector is 375cos353 + 42cos20 = about 411.67

And the y component of the resultant vector is 375sin353 + 42sin20 = about -31.336

And the magnitude of the resultant vector = √[(411.67)^2 + (-31.336)^2] = about 412.86

And the angle of the resultant is given by

tan^{-1} (-31.336 / 411.67) = about -4.35° = 355.65° = S85.65°E (in terms of heading)

So....the speed of the drone is 412.86 mph in the direction of S85.65°E

CPhill
Nov 25, 2014

#1**+5 **

Best Answer

I'll do this one with vectors

S83°E = 353°

E20°N = 20°

So, the first vector is <375cos353 , 375sin353 > ....and the second vector is <42cos20, 42sin20>

So the x component of the resultant vector is 375cos353 + 42cos20 = about 411.67

And the y component of the resultant vector is 375sin353 + 42sin20 = about -31.336

And the magnitude of the resultant vector = √[(411.67)^2 + (-31.336)^2] = about 412.86

And the angle of the resultant is given by

tan^{-1} (-31.336 / 411.67) = about -4.35° = 355.65° = S85.65°E (in terms of heading)

So....the speed of the drone is 412.86 mph in the direction of S85.65°E

CPhill
Nov 25, 2014