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Consider a crossbow bolt shot straight upward from the ground on a certain planet with an initial velocity of 46 m/s. Because of linear air resistance, its velocity function v(t) satisfies the following initial value problem. dv = - (0.04)v - 9.6, v(0) = 46 This initial value problem has the exact solution v(t) = 286 e 20 - 240. Use a calculator or computer implementation of the improved Euler method to approximate v(t) for 0 sIS 10 using both n= 50 and n = 100 subintervals. Display the results at intervals of 1 second. Do the approximations agree both with each other and with the exact solutions? If the exact solutions were unavailable, explain how you could use the improved Euler method to approximate closely (a) the bolt's time of ascent to its apex and (b) its impact velocity after 9.04 s in the air? Use the improved Euler method to approximate v(t) for 0 StS 10 using both n = 50 (h = 0.2) and n= 100 (h = 0.1) subintervals. Complete the table below. (Round to two decimal places as needed.) 1 2 5 6 9 10 Vn, h-0.2

Consider a crossbow bolt shot straight upward from the ground on a certain planet with an initial velocity of 46 m/s. Because of linear air resistance, its velocity function v(t) satisfies the following initial value problem. dv = - (0.04)v - 9.6, v(0) = 46 This initial value problem has the exact solution v(t) = 286 e 20 - 240. Use a calculator or computer implementation of the improved Euler method to approximate v(t) for 0 sIS 10 using both n= 50 and n = 100 subintervals. Display the results at intervals of 1 second. Do the approximations agree both with each other and with the exact solutions? If the exact solutions were unavailable, explain how you could use the improved Euler method to approximate closely (a) the bolt's time of ascent to its apex and (b) its impact velocity after 9.04 s in the air? Use the improved Euler method to approximate v(t) for 0 StS 10 using both n = 50 (h = 0.2) and n= 100 (h = 0.1) subintervals. Complete the table below. (Round to two decimal places as needed.) 1 2 5 6 9 10 Vn, h-0.2

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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Consider a crossbow bolt shot straight upward from the ground on a certain planet with an initial velocity of 46 m/s. Because of linear air resistance, its velocity function v(t) satisfies the following initial value problem. dv (0.04)v – 9.6, v(0) = 46 dt t - 240. Use a calculator or computer implementation of the improved Euler method to approximate v(t) for 0<t<10 using both n= 50 and n= 100 subintervals. Display the results at intervals of This initial value problem has the exact solution v(t) = 286 e 1 second. Do the approximations agree both with each other and with the exact solutions? If the exact solutions were unavailable, explain how you could use the improved Euler method to approximate closely (a) the bolt's time of ascent to its apex and (b) its impact velocity after 9.04 s in the air? Use the improved Euler method to approximate v(t) for 0<t<10 using bothn= 50 (h = 0.2) and n = 100 (h = 0.1) subintervals. Complete the table below. (Round to two decimal places as needed.) tn 1 2 3 4 6 7 8 9 10 Vn, h= 0.2
Transcribed Image Text:Consider a crossbow bolt shot straight upward from the ground on a certain planet with an initial velocity of 46 m/s. Because of linear air resistance, its velocity function v(t) satisfies the following initial value problem. dv (0.04)v – 9.6, v(0) = 46 dt t - 240. Use a calculator or computer implementation of the improved Euler method to approximate v(t) for 0<t<10 using both n= 50 and n= 100 subintervals. Display the results at intervals of This initial value problem has the exact solution v(t) = 286 e 1 second. Do the approximations agree both with each other and with the exact solutions? If the exact solutions were unavailable, explain how you could use the improved Euler method to approximate closely (a) the bolt's time of ascent to its apex and (b) its impact velocity after 9.04 s in the air? Use the improved Euler method to approximate v(t) for 0<t<10 using bothn= 50 (h = 0.2) and n = 100 (h = 0.1) subintervals. Complete the table below. (Round to two decimal places as needed.) tn 1 2 3 4 6 7 8 9 10 Vn, h= 0.2
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