The length of the string of a pendulum, cap l , can be determined using the function cap l times p is equal to 9 point 8 times open paren p over 2 pi close paren squared , where p is the period of the pendulum. The velocity at the bottom of the pendulum can be modeled by the function v times cap l is equal to square root of 19 point 6 liters Which function can be used to find the velocity at the bottom of the pendulum released from the same angle for any period, p ?
Answer
A
v times open paren cap l times p close paren is equal to square root of 192 point 0 8 p over 2 pi end root
B
v times open paren cap l times p close paren is equal to p over 2 pi square root of 192 point 0 8
C
v times open paren cap l times p close paren is equal to p over 2 pi square root of 19 point 6
D
v times open paren cap l times p close paren is equal to square root of 19 point 6 p over 2 pi end root
Explanation
Substitute the pendulum length, 9.8(p/2π)², into the velocity rule v = √(19.6l). This gives v = √(19.6 × 9.8 × (p/2π)²) = √192.08 × p/(2π), since a period p is positive. Therefore, the function is v(l(p)) = (p/2π)√192.08, which is choice B.
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