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Solved: A certain volcano on earth can eject rocks
Chapter 2, Problem 81P(choose chapter or problem)
Problem 81P
A certain volcano on earth can eject rocks vertically to a maximum height H. (a) How high (in terms of H) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s2; ignore air resistance on both planets. (b) If the rocks are in the air for a time T on earth, for how long (in terms of T) would they be in the air on Mars?
Questions & Answers
QUESTION:
Problem 81P
A certain volcano on earth can eject rocks vertically to a maximum height H. (a) How high (in terms of H) would these rocks go if a volcano on Mars ejected them with the same initial velocity? The acceleration due to gravity on Mars is 3.71 m/s2; ignore air resistance on both planets. (b) If the rocks are in the air for a time T on earth, for how long (in terms of T) would they be in the air on Mars?
ANSWER:
Solution 81P
Introduction
The stone will be thrown up by volcano with some amount of energy. The energy will be equal to the potential energy of the stone at its maximum height.
Whether it is on earth or mars, the stone will be thrown up with same initial kinetic energy. So the potential energy at the maximum height will be same for both on earth and mars. Using this relation we will calculate the height in mars.
Step 1
(a) Let us consider mass of a stone is . So the energy of the stone with which it was thrown is
Where, is the acceleration due to gravity on earth.
Now if the same stone is thrown in the mars, if it reaches the height then the potential energy is
Now equating the above energies, we can write that
Now, as given in the problem,
So the height on the mars is given by
So the volcano can throw 2.6 times the height on the earth.