Question

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?

Answer 1

Answer:

Magnitude = 3.64 × $10^6$  

စ = 43.9°

Explanation:

given data

ship to travel = 1.7 × $10^6$    kilometers

turn = 70°

travel an additional = 2.7 × $10^6$   kilometers

solution

we will consider here

Px = 1.7 × $10^6$  

Py = 0

Qx =2.7 × $10^6$  cos(70)

Qy= 2.7 × $10^6$  sin(70)

so that

Hx = Px + Qx    ............1

Hx = 2.62 × $10^6$  

and

Hy = Py + Qy      ..........2

Hy = 2.53 × $10^6$  

so Magnitude = $\sqrt{((2.62 \times 10^6 )^2+(2.53 \times 10^6)^2)}$

Magnitude = 3.64 ×  

so direction  will be

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

tan စ  = $\frac{2.53}{2.62}$

tan စ  = 0.9656

စ = 43.9°