Homework-5-s11

Homework-5-s11 - and the jumper’s initial vertical speed...

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Homework 5 Assignment Date: Wednesday (03/14/2011) Collection Date: Wednesday (03/23/2011) Grade: Each problem is worth 10 points Problem 5.1: Suppose that a projectile is fired straight upward from the surface of the earth with initial velocity ° 0 and assume its height ± ( ² ) above the surface satisfies the initial value problem ⎧± ′′ = ³´ ( ± + µ ) 2 − ¶· ¸¹ ± (0) = 0 ±º (0) = ° 0 Compute the total amount of time for the projectile to stay in sky from launch till re-touch of the ground. Also, please compute the velocity at the instance when the projectile re-touches ground. In the above, ³ , ´ , µ , ° 0 , are all given constants. Problem 5.2: A guy (of body mass » ) jumps out of a horizontally flying plane of speed ° 0 at height ¼ . The horizontal component of the jumper’s initial velocity is equal to that of the plane’s
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Unformatted text preview: and the jumper’s initial vertical speed can be regarded as 0. The air resistance is ½ | ° ⃗ | with the parachute open where ½ is a given constant and | ° ⃗ | = ° ¾ 2 + ° ¹ 2 is the magnitude of jumper’s velocity. You may ignore the air resistance when the parachute is closed. Please compute the jumper’s velocity as a function of height if the jumper opens his/her parachute at 1 2 ¼ . Problem 5.3 : Check if the following three functions are linearly independent: 2 ¿ 2 , 3x 3 , 8 ¿ 3 − 27 ¿ 2 Problem 5.4 : Find the general solution of the following equation: ± ′′ − ± ′ − 12 ± = 0 Problem 5.5: Find the general solution of the following equation: ± ′′ − 3 ± ′ − 18 ± = 0 Problem 5.6 : Find the general solution of the following equation ¿ 2 ± ′′ + 2 ¿± ′ − 3 ± = 0...
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