Consider the crossbow bolt of Example in Section, shot straight upward from the ground wit...

Consider the crossbow bolt of Example in Section, shot straight upward from the ground with an initial velocity of 49 m/s. Because of linear air resistance, its velocity function v(t) satisfies the initial value problem

with exact solution v(t) = 294e−t/25 − 2455. 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 1 second. Do the two approximations—each rounded to two decimal places—agree both with each other and with the exact solution? If the exact solution were unavailable, explain how you could use the improved Euler method to approximate closely (a) the bolt’s time of ascent to its apex (given in Section 1.8 as 4.56 s) and (b) its impact velocity after 9.41 s in the air.