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2. Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv m = dt mg -kv², k > 0 where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N. s/m after: a) 10 s b) 100 s c) 1000 s

2. Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv m = dt mg -kv², k > 0 where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N. s/m after: a) 10 s b) 100 s c) 1000 s

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv m = dt mg - kv², k > 0 where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N.s/m after: a) 10 s b) 100 s c) 1000 s
Transcribed Image Text:2. Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv m = dt mg - kv², k > 0 where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N.s/m after: a) 10 s b) 100 s c) 1000 s
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