A spaceship is traveling through deep space towards a space station and needs to make a course correction to go around a nebula. The captain orders the ship to travel 1.7 ✕ 106 kilometers, then turn 70° and travel an additional 2.7 ✕ 106 kilometers to reach the space station. If the captain had not ordered a course correction, what would have been the magnitude and direction of the path of the spaceship if it has traveled through the nebula?

Magnitude = 3.64 ×  

စ = 43.9°

Explanation:

given data

ship to travel = 1.7 ×    kilometers

turn = 70°

travel an additional = 2.7 ×   kilometers

solution

we will consider here

Px = 1.7 ×  

Py = 0

Qx =2.7 ×  cos(70)

Qy= 2.7 ×  sin(70)

so that

Hx = Px + Qx    ............1

Hx = 2.62 ×  

and

Hy = Py + Qy      ..........2

Hy = 2.53 ×  

so Magnitude =

Magnitude = 3.64 ×  

so direction  will be

tan စ = Hy ÷ Hx    ......................3

tan စ  =

tan စ  = 0.9656

စ = 43.9°

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