Solution Found!
Unreasonable ResultsSuppose you wish to shoot supplies
Chapter 3, Problem 68(choose chapter or problem)
Problem 68PE
Unreasonable Results
Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height? (d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.
Questions & Answers
QUESTION:
Problem 68PE
Unreasonable Results
Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height? (d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.
ANSWER:
Solution 68 PE
a.)
Step 1 of 4
The velocity (v) with which the supplies must be launched can be found by applying law of conservation of energy, at the highest point the kinetic energy of the supplies is totally converted into gravitational potential energy.
=
where, m = mass of the supplies in kg
v = velocity of the supplies in kg
h = distance between the Earth’s surface
and astronauts in orbit in m
Solving for v,
Substituting 9.8 m/s2 for g and 36000103 m for h,
= 26563.132 m/s
= 26.56 km/hr
Therefore, the velocity of the supplies launched is 26.56 km/hr
b.)