Terminal Velocity Terminal velocity is the maximum speed that a body falling through air can reach (because of air resistance) Terminal velocity is given by the formula v t = 2 m g C p A ,where m is the mass of the falling object, g is acceleration due to gravity (≈ 9.81 meters per second 2 ), C is a drag coefficient with 0.5 ≤ C ≤ 1.0, p is the density of air (≈ 1.2kg/m 3 ), and A is the cross-sectional area of the object Suppose that a raindrop whose radius is 1 5 mm falls from the sky The mass of the raindrop is given by m = 4 3 π r 3 p w , where r is its radius and p w = 1000kg/m 3 . The cross-sectional area of the raindrop is A = π r 2 . a. Substitute the formulas for the mass and area of a raindrop into the formula for terminal speed, and simplify the expression b. Determine the terminal velocity of a raindrop whose radius is 0 0015 m with C = 0.6.
Terminal Velocity Terminal velocity is the maximum speed that a body falling through air can reach (because of air resistance) Terminal velocity is given by the formula v t = 2 m g C p A ,where m is the mass of the falling object, g is acceleration due to gravity (≈ 9.81 meters per second 2 ), C is a drag coefficient with 0.5 ≤ C ≤ 1.0, p is the density of air (≈ 1.2kg/m 3 ), and A is the cross-sectional area of the object Suppose that a raindrop whose radius is 1 5 mm falls from the sky The mass of the raindrop is given by m = 4 3 π r 3 p w , where r is its radius and p w = 1000kg/m 3 . The cross-sectional area of the raindrop is A = π r 2 . a. Substitute the formulas for the mass and area of a raindrop into the formula for terminal speed, and simplify the expression b. Determine the terminal velocity of a raindrop whose radius is 0 0015 m with C = 0.6.
Solution Summary: The author explains the simplified formula for the terminal speed of the raindrop.
Terminal Velocity Terminal velocity is the maximum speed that a body falling through air can reach (because of air resistance) Terminal velocity is given by the formula
v
t
=
2
m
g
C
p
A
,where m is the mass of the falling object, g is acceleration due to gravity (≈ 9.81 meters per second2), C is a drag coefficient with 0.5 ≤ C ≤ 1.0, p is the density of air (≈ 1.2kg/m3), and A is the cross-sectional area of the object Suppose that a raindrop whose radius is 1 5 mm falls from the sky The mass of the raindrop is given by
m
=
4
3
π
r
3
p
w
, where r is its radius and
p
w
= 1000kg/m3. The cross-sectional area of the raindrop is A = πr2.
a. Substitute the formulas for the mass and area of a raindrop into the formula for terminal speed, and simplify the expression
b. Determine the terminal velocity of a raindrop whose radius is 0 0015 m with C = 0.6.
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY