
Concept explainers
(a)
The distance between the astronaut and asteroid.
(a)

Answer to Problem 171P
The distance between the astronaut and asteroid is
Explanation of Solution
The mass of the astronaut is
Write the expression to calculate the acceleration of the astronaut.
Here, a is the acceleration of the astronaut, F is the force on the astronaut and M is the mass of the astronaut.
Substitute
Write the expression to calculate the acceleration of the asteroid.
Here,
Substitute
Write the expression to calculate the distance travelled by the astronaut.
Here, x is the distance moved by the astronaut, u is the initial speed of the astronaut and t is the time taken during the application of force.
Substitute
Write the expression to calculate the distance travelled by the asteroid.
Here,
Substitute
Write the expression to calculate the speed of the astronaut.
Here, v is the speed of the astronaut.
Substitute
Write the expression to calculate the speed of the asteroid.
Here,
Substitute
Write the expression to calculate the distance moved by the astronaut for
Here, s is the distance moved by the astronaut and T is the time taken after the force.
Substitute
Write the expression to calculate the distance moved by the asteroid for
Here,
Substitute
Write the expression to calculate the distance between the astronaut and asteroid.
Here, X is the distance between astronaut and asteroid.
Substitute
Conclusion:
Therefore, the distance between the astronaut and asteroid is
(b)
The relative speed between astronaut and asteroid.
(b)

Answer to Problem 171P
The relative speed between astronaut and asteroid is
Explanation of Solution
Both are travelling in opposite direction. Thus the speed with respect one another is the sum of the speed of individual one.
Write the expression to calculate the relative speed between astronaut and asteroid.
Here, V is the relative speed between astronaut and asteroid.
Substitute
Conclusion:
Therefore, the relative speed between astronaut and asteroid is
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Chapter 4 Solutions
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