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.
A metal plate is heated so that its temperature at a point (x, y) is T(x, y) = x²e2x+3¥).
A bug is placed at the point (1, 1).
The bug heads toward the point (2, –4). What is the rate of change of temperature in this direction?
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
per unit length
Consider the direction the bug should head to warm up at the fastest rate. Find the rate of change of temperature in this direction.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
per unit length
Consider the direction the bug should head to cool off at the fastest rate. Find the rate of change of temperature in this direction.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
per unit length
A car had the velocity in the image attached. Help find how far did the car travel from t=0 to t=30 seconds
A skydiver weighing 292 lbf (including equipment) falls vertically downward from an altitude of 4000 ft and opens the parachute after
10s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is 0.77 |v| when the parachute is
closed and 10|v| when the parachute is open, where the velocity v is measured in ft/s.
Use g = 32 ft/s². Round your answers to two decimal places.
(a) Find the speed of the skydiver when the parachute opens.
v(10) = i
(b) Find the distance fallen before the parachute opens.
x(10) = i
VL
(c) What is the limiting velocity v after the parachute opens?
=
ft/s
i
ft
ft/s
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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