Question

Missile Defense Systenm You are designing a missile defense system that will shoot down incoming missiles that pass over a perimeter defense post. I he set-up Is shown below. An incoming missile passes directly above the defense base. Radar at the hase can measure the height, h, and speed, V, of the incoming missile. Your Patriot Rocket is set to fire at an angle of 49.0 degrees from vertical. You design the Patrniat Rocket so the magnitude of its acceleration is given by where A can be set on your Patriot Rocket as it is fired, b-0.30 s-1 and t-0 when it is fired. The direction of your Patriot Rockets vector acceleration stays at the same angle, θ for the entire trip. If an incoming missile passes over the defense base at a helght of 4.40 km and at a constant speed of 679.0 m/s (this means that V Is constant), solve for the value of A your Patriot Rocket must have in order to hit the Incoming missile. You will also need to enter results rom intermediate steps of your calculation, in uding the horizontal distance ΔΧ ram the launch station to the impact position and the time at impact.

$\Delta x = 5.062 \times 10^3 \textit{m}$

$t_{f} = 7.455 s$

$\textrm{Find } \mathit{A}$

Answer 1

Given: a_2 = A e^-bt d^2x/dt^2 = A e- b t x = A/(- b)^2 e^-bt + c x = A/b^2 e^-bt + c At t = 0s, x = 0 m 0 = A/b^2 e^-b(0) + c c = 0 At t = 7.4555, x = 5.062 times 10^3 m, 5.062 Km = A/(0.30 S^-1) e^-(0.30)(7.455) + 0 A = (5.062 times 10^3) (0.30)^2/e^-(0.30)(7.455) A = 4264.46 m/s^2