Consider now the crossbow bolt of Example 3 in Section 1.8. It still is shot straight upwa...

Consider now the crossbow bolt of Example 3 in Section 1.8. It still is shot straight upward from the ground with an initial velocity of 49 m/s, but because of air resistance proportional to the square of its velocity, its velocity function v(r) satisfies the initial value problem

The symbolic solution discussed in Section 1.8 required separate investigations of the bolt’s ascent and its descent, with u(t) given by a tangent function during ascent and by a hyperbolic tangent function during descent. But the improved Euler method requires no such distinction. Use a calculator or computer implementation of the improved Euler method to approximate v(t) for 0 ≦t≦ 10 using both n = 100 and n = 200 subintervals. Display the results at intervals of 1 second. Do the two approximations—each rounded to two decimal places—agree with each other? If an 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 4.61 s) and (b) its impact velocity after 9.41 s in the air.