Hand writing solution please.

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 = 0 to time t = t1. Before and after the bullet exits the railgun, it experiences the normal resistance due to its environment, i.e. FR = no(t), where v(t) is the instanteneous speed of the bullet. The one-dimensional trajectory of the bullet is then described by the differential equation " ( 7 ) , fill - ( 17 + 7 - )0 (7) 01 = (7), fu with y(0) = 0 = y'(0). We would like to use this to see if the Gundam can hit a moving target. a) Apply the Lapalce transform on both sides and obtain the corresponding equation for Lly(t)] (s). Fill in the gaps below to give your answer, i.e., Lly(t) ] (s) = F(1-e -tis) P(s) where P(s) = X8 + XS-+ XS+ Submit part Score: 0/4 Unansweredb) Letting t1 = 5, m = 1, and n = 1, the expresion can be written as Lly(t) ](s) = Fx (1-e-t2s) S X 1 ms- +ns' or (keeping the x in the same place) as Lly(t)](s) = Fx L[A(t)](s) x L[B(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.C) Use the convolution theorem to solve to find the solution y(t) of the differential equation. What is the equation for y(t) for t > t1? y(t) /F = [Hint: it should be a linear combiantion of two exponentials and a cosntant] Plot y(t) as a function of t for a fixed 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 =