Solve the following ODE proble using Laplace. [ Ignoring units for simplicity] The average electromagnetic railgun on a Gundam consists of a frictionless, open-to-the-environment, rail in which a projectile of mass m is imparted a force F from time t : U to time t : t1. Before and after the bullet exits the railgun, it experiences the normal resistance due to its environment, i.e. FR : 1711(15) where v(t) is the instanteneous speed of the bullet. The one-dimensional trajectory of the bullet is then described by the differential equation ins/"(15): F903) 9(7t + t1) , ny'(t), with y(0) : 0 : y'(0). We would like to use this to see if the Gundam can hit a moving target. 8) Apply the Lapalce transform on both sides and obtain the corresponding equation for L[y(t)](s). Fill in the gaps below to give your answer, i.e., We : where P(s) : x33+ xs2+ xs+ Submit part Score: 014 Unanswered b) Letting t1 = 5, m = 1, and n = 1, the expresion can be written as Lly(t) ](s) = Fx (1-e-25 ) 1 X ms- +ns' or (keeping the x in the same place) as Lly(t)](s) = Fx L[A(t)](s) x LIB(t) ](s), where A(t) = o O(t - 5) + 8(t) 0 8(t) - 8(t -5) 0 0(t) - 0(t -5) 08(t) and B(t) = Hint: ForB(t) you will need to use partial fractions.Use the convolution theorem to solve to nd the solution y(t) of the differential equation. What is the equation for y(t) for t 2 t1? arm/F = [Hint it should be a linear combiantion of two exponentials and a cosntant] Plot y(t) as a function of t for a xed F. d) If one want the Gundam to hit a moving target that will be at a distance of 100 at time 20, what should be the value of F? (Enter the value of F to two decimals) F