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Question 152836This question is from textbook basic technical mathematics with calculus
: A satellite is to be launched from a space shuttle. It is calculated that the satelite's speed will be 24,200 km/h if launched directly ahead of the shuttle or 21,400 km/h if launched directly to the rear of the shuttle. What is the speed of the shuttle and the launching speed of the satellite relative to the shuttle?
This question is from textbook basic technical mathematics with calculus
Answer by orca(409)   (Show Source):
You can put this solution on YOUR website! Let x be the speed of the shuttle.
Let y be the satellite's launching speed relative to the shuttle.
So if launched ahead of the shuttle the satellite's speed is x + y.
if launched to the rear of the shuttle the satellite's speed is x - y.
Thus according to the given information:
x + y = 24,200 ...........(1)
x - y = 21,400 ...........(2)
Adding (1) and (2) together, we have
x + y + x - y = 24,200 + 21,400
2x = 45,600
x = 22,800
Substituting x = 22,800 into equation (1), we have
22,800 + y = 24,200
Solving for y,we obtain
y = 24,200 - 22,800 = 1,400
Therefore the speed of the shuttle is 22,800 km/h, and the satellite's launching speed relative to the shuttle is 1,400 km/h
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