Unformatted text preview: result? Which one contributes the least? 3. A missile leaves the ground with an initial velocity v forming an angle ϕ with the vertical. The maximum desired altitude is h = αR , where R is the radius of the earth. The laws of mechanics can be used to show that sin( ϕ ) = (1 + α ) s 1-α 1 + α ± v e v ² 2 , where v e is the escape velocity of the missile. It is desired to ﬁre the missile and reach the design maximum altitude with an accuracy of ± 2%. Determine the admissible range of values for ϕ , both using ﬁrst-order (linear) error analysis, and exactly, if v e /v = 2 and α = . 25. 4. Give the condition numbers κ for the following functions: a. f ( x ) = 1 p | x + 1 | -1 , for x = . 0001 , b. f ( x ) = e-x , for x = 9 , c. f ( x ) = p x 2 + 1-x, for x = 200 , d. f ( x ) = e x-1 x , for x = . 01 , e. f ( x ) = sin( x ) 1 + cos( x ) , for x = 1 . 001 π....
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- Spring '05
- Numerical Analysis, Ratio, Fundamental physics concepts, 0.005 m