Unformatted text preview: v 2 2 = gR 2 r + K, where K is an arbitrary constant. We can ²nd the constant K by using the initial value as follows: K = v 2 2 − gR 2 R = v 2 2 − gR. Substituting this formula for K and solving for the velocity we obtain v 2 = 2 gR 2 r + v 2 − 2 gR. (d) In order for the velocity of the projectile to always remain positive, (2 gR 2 /r ) + v 2 must be greater than 2 gR as r approaches in²nity. This means lim r →∞ ² 2 gR 2 r + v 2 ³ > 2 gR ⇒ v 2 > 2 gR. Therefore, v 2 − 2 gR > 0. 136...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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