Dynamics_Part22

Dynamics_Part22 - Problem Set 3: Problem 3. Problem: A test...

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Problem Set 3: Problem 3. Problem: A test projectile is fired horizontally into a viscous liquid with initial velocity v o . The drag force, D , on the projectile is D = mkv 2 ,where m is the projectile’s mass, v is instantaneous velocity and k is a constant of dimensions length 1 . Assume the motion is so rapid that any vertical deflection due to gravity is negligible. (a) Determine the velocity of the projectile in terms of v o , k and t and compute the time at which the projectile’s speed is 1 2 v o . (b) Determine the projectile’s instantaneous position, x , as a function of v , v o and k . Solution: Newton’s Second Law tells us that
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