Solution: First, you should express the acceleration of the ball as a=dv/dt=g+kv, where K = K/M = 0.03 ÷ 45 kg =11500 kg. The differential formula dv/dt=g+kv can be written as dv/(g+kv)=dt, that is to say, d(g+kv)/(g+kv)=kdt, and the two sides can be integrated to get: ln|g+kv|=kt+C, according to the meaning of the question, because the direction of resistance F and gravity G is opposite to the initial velocity, k =-. So at the peak time, c = ln |-9.8-60 ÷1500 | ≈ 2.40855856866, v=0, and substitute it to find t = (ln | g |-c)/k = (ln 9.8-ln 9.84) ×/kloc. According to this, the maximum lifting height can be obtained, s = ∫ VDT = ∫ [e (kt+c)-g] dt/k = e (kt+c)/k&; Sup2-gt/k+C', and when t=0 and s=0, thus c' =-(EC)/k&; sup2=-9.84× 1500。 Sup2=-22 140000. Substituting the time t of rising to the highest point, the maximum rising height Hmax≈ 183m can be obtained.