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Differential EquationsMediumNumerical Methods: Euler to Runge–Kutta

Numerical Methods: Euler to Runge–Kutta · Medium problem

A ball bearing dropped into thick syrup falls according to v′=9.8−0.4vv' = 9.8 - 0.4v (v in m/s downward, t in seconds), v(0)=0v(0) = 0. Using Euler's method with h=1h = 1 s, estimate v(1)v(1) and v(2)v(2), then use the trapezoidal rule on those three velocity values (v0,v1,v2v_0, v_1, v_2, spacing h=1h = 1) to estimate how far the bearing has fallen after 22 seconds. Express your answer as a decimal.