A spaceship maneuvering near Planet Zeta is located at vector r = (600 hat i - 4

Question

A spaceship maneuvering near Planet Zeta is located at vector r = (600 hat i - 400 hat j + 200 hat k) times 10^3 km, relative to the planet, and traveling at vector v = 9500 hat i m/s. It turns on its thruster engine and accelerates with vector a = (40 hat i - 20 hat k) m/s^2 for 35 min. What is the spaceship's position when the engine shuts off? Give your answer as a vector measured in km. Express your answer in terms of the unit vectors hat i, hat j, and hat k. Use the 'unit vector' button to denote unit vectors in your answer.

Explanation / Answer

From kinematic equations

X2-x1= UT+1/2at^2

X2 = 10^8(6i4j+2k)+9500*35*60i+1/2*(40i-20k)*35*35*60*60

X2 =10^8(7.0815i-4j+1.559k)

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