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14x10 1. The velocity of a rocket is given by v(t) = 2000 In -9.8t,0≤t≤30 where 14×10¹ - 2100t v is given in m/s and t is given in seconds. At t=16 s and using At=2 s, a. Use forward difference, backward difference and central difference approximations of the first derivative of v(t) to determine the acceleration of the rocket. b. If the true value of the acceleration at t=16 s is 29.674 m/s², calculate the absolute relative true error for each approximation obtained. What can you conclude from these values of the relative errors?

14x10 1. The velocity of a rocket is given by v(t) = 2000 In -9.8t,0≤t≤30 where 14×10¹ - 2100t v is given in m/s and t is given in seconds. At t=16 s and using At=2 s, a. Use forward difference, backward difference and central difference approximations of the first derivative of v(t) to determine the acceleration of the rocket. b. If the true value of the acceleration at t=16 s is 29.674 m/s², calculate the absolute relative true error for each approximation obtained. What can you conclude from these values of the relative errors?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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14x10¹ 1. The velocity of a rocket is given by v(t) = 2000 In -9.8t, 0≤t≤30 where 14×10¹ - 2100t v is given in m/s and t is given in seconds. At t=16 s and using At= 2 s, a. Use forward difference, backward difference and central difference approximations of the first derivative of v(t) to determine the acceleration of the rocket. b. If the true value of the acceleration at t=16 s is 29.674 m/s², calculate the absolute relative true error for each approximation obtained. What can you conclude from these values of the relative errors? 2. Determine the second derivative of f(x)=x²e²* at x = -2 with a step-size of h=0.50 using Central difference approach.
Transcribed Image Text:14x10¹ 1. The velocity of a rocket is given by v(t) = 2000 In -9.8t, 0≤t≤30 where 14×10¹ - 2100t v is given in m/s and t is given in seconds. At t=16 s and using At= 2 s, a. Use forward difference, backward difference and central difference approximations of the first derivative of v(t) to determine the acceleration of the rocket. b. If the true value of the acceleration at t=16 s is 29.674 m/s², calculate the absolute relative true error for each approximation obtained. What can you conclude from these values of the relative errors? 2. Determine the second derivative of f(x)=x²e²* at x = -2 with a step-size of h=0.50 using Central difference approach.
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