April 13, 2009 WARM-UPS ~ 7.2 PRACTICE PROBLEMS
1. The circular velocity v in miles per hour, of a satellite orbiting Earth is given by the formula v 
1.24  1012
,
r
where r is the distance in miles from the satellite to the center of the Earth. How much greater is the velocity of a
satellite orbiting at an altitude of 100 mi than one orbiting at an altitude of 200 mi? (The radius of the earth is 3950
mi.)
2. A string of a certain length and tension on a musical instrument has frequency f, in hertz or vibrations per second,
and is given by the formula f 
1 6.6  10 8
, where m is the mass of the string in grams. How much greater is
94
m
the mass of a string with a frequency of 300 hertz than one with 350 hertz.
April 13, 2009 WARM-UPS ~ 7.2 PRACTICE PROBLEMS
3. The circular velocity v in miles per hour, of a satellite orbiting Earth is given by the formula v 
1.24  1012
,
r
where r is the distance in miles from the satellite to the center of the Earth. How much greater is the velocity of a
satellite orbiting at an altitude of 100 mi than one orbiting at an altitude of 200 mi? (The radius of the earth is 3950
mi.)
4. A string of a certain length and tension on a musical instrument has frequency f, in hertz or vibrations per second,
and is given by the formula f 
1 6.6  10 8
, where m is the mass of the string in grams. How much greater is
94
m
the mass of a string with a frequency of 300 hertz than one with 350 hertz.
April 13, 2009 WARM-UPS ~ 7.2 PRACTICE PROBLEMS
1.24  1012
5. The circular velocity v in miles per hour, of a satellite orbiting Earth is given by the formula v 
,
r
where r is the distance in miles from the satellite to the center of the Earth. How much greater is the velocity of a
satellite orbiting at an altitude of 100 mi than one orbiting at an altitude of 200 mi? (The radius of the earth is 3950
mi.)
6. A string of a certain length and tension on a musical instrument has frequency f, in hertz or vibrations per second,
and is given by the formula f 
1 6.6  10 8
, where m is the mass of the string in grams. How much greater is
94
m
the mass of a string with a frequency of 300 hertz than one with 350 hertz.