PHY321-Practice-MT1 - meters), before it hits the ground?...

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Practice Midterm Exam #1 Total points = 25. Show all of your work! 1. [6 points] If A = 5 i and B = 3 i + 4 j find (a) [2] A.B (b) [2] A x B (c) [2] The angle θ AB between A and B . 2. [7 points] Suppose that the frictional force on an object of mass m traveling through a fluid is proportional to the cube of the velocity: F = -mkv 3 where k is a constant (and m is included to make the math a bit easier). (a) [4] Find the velocity as a function of time, assuming that the initial velocity is v 0 at time t = 0. Neglect gravity. (b) [3] After what time has the velocity slowed to half the initial velocity? Note: There is another question on the next page!
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3. [12 points] An object of mass m 0 = 30 kg. is launched at time t = 0 with a horizontal velocity of 40.0 m/s. (There is initially no vertical component to the velocity.) (a) [2] What is the kinetic energy of the object, K i (in Joules)? (b) [4] If the initial height of the object is h = 1000 m, what is the expected range, R (in
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Unformatted text preview: meters), before it hits the ground? (Use the x origin as the point of launch, and use g = 9.81 m.s-2 .) Unfortunately, immediately after the launch, the object explodes into two fragments (each of mass equal to one-half of the original object (m 1 = m 2 = m /2 = 15 kg) i.e. we are neglecting the mass of the explosive material). The explosion contributes an additional energy of E ex = 10.0 kJ (10000 Joules). The two fragments are ejected at right angles to the original line of flight of the initial object i.e. vertically in the CM frame, fragment m 1 straight up and fragment m 2 straight down. (c) [6] Immediately after the explosion, what is the velocity (magnitude and angle relative to the horizontal) of fragment m 1 relative to an observer on the ground?...
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This note was uploaded on 03/19/2008 for the course PHY 321 taught by Professor B.pope during the Spring '08 term at Michigan State University.

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PHY321-Practice-MT1 - meters), before it hits the ground?...

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