Question
The escape speed of a projectile on the surface of earth is 11.2km/s. A body is projected out with thrice this speed. What is the speed of body far away from the earth? Ignore the presence of the sun and other planets.
Solution
Let v be the velocity of projection and v' the velocity of the body at infinity.
According to the principle of law of conservation of energy,
Total energy at the surface of earth = Total energy at infinity
i.e.
...(1)
If,
Then,
Therefore,
...(2)
From equation (1) and (2),
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... (3)
Here, we have that the body is projected with thrice the speed of escape velocity.
i.e.,![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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Therefore, putting this in equation (3),
We have,![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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This is the required speed of the body far away from the earth.
According to the principle of law of conservation of energy,
Total energy at the surface of earth = Total energy at infinity
i.e.
...(1)If,
Then,
Therefore,
...(2)From equation (1) and (2),
... (3)Here, we have that the body is projected with thrice the speed of escape velocity.
i.e.,
Therefore, putting this in equation (3),
We have,
This is the required speed of the body far away from the earth.
