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 2.7 106 kilometers before turning 70° and traveling 2.5 106 kilometers before assuming the path towards 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 had traveled through the nebula? magnitude 1008.57 Incorrect: Your answer is incorrect. Did you find the components of each vector and then add them? km direction ° counterclockwise from the +x-axis

Explanation / Answer

here,

a = 2.7 * 10^6 km

a = 2.7 * 10^9 m

b = 2.5 * 10^6 km

b = 2.5 * 10^9 m

theta = 70 degree

R = sqrt(a^2 + b^2 + 2 * a * b * cos(theta))

R = sqrt( (2.7 * 10^9)^2 + (2.5 * 10^9)^2 + 2 * 2.7 * 10^9 *2.5 * 10^9 * cos(70))

R = 4.26 * 10^9 m

direction = arctan(a * sin(theta)/(b + a * cos(theta)))

direction = arctan(2.7 * 10^9 * sin(70)/(2.5 * 10^9 + 2.7 * 10^9 * cos(70)))

direction is 36.54 degree

the magnitude of path is 4.26 * 10^6 km and 36.54 degree counterclockwise from the +ve x axis

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