A spaceship is traveling through deep space towards a space station and needs to

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 2.5 x 10 kilometers before turning 7 and traveling 1.9 1 06 kilometers before assuming the path towards the space station. If the captain had not ordered a course correction, what would have been the magnitude in meters and direction in degrees counterclockwise from the +x-axis) of the path of the spaceship if it had traveled through the nebula? space station nebula spaceship magnitude km directior o counterclockwise from the +x-axis Additional Materials Reading Tutorial Submit Assignment Save Assignment Progress

Explanation / Answer

Assume that the "i" vector is the original course.
resultant R = [(2.5e6 + 1.9e6*cos70º) i + 1.9e6*sin70º j] km
R = [3.149e6 i + 1.79e6 j] km

so |R| = (3.149² + 1.79²) * 1e6 km = 3.6229e6 km
and angle A = arctan(1.79/3.149) = 29.61º from the original heading.

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