Question

Ground-based air defence systems play an important part in ensuring the safety and security against any possible attacks from the air. For example, a few of such systems were deployed during the Trump-Kim summit held in Singapore on 12 June this year. As shown in Figure 2(a), a particular air defence system consists of an interceptor missile that can be launched from a Mobile Firing Unit (MFU). Actual systems will require very precise engineering involving interceptor missiles that can lock on targets but here, we will only do a very simplified analysis. We assume that the interceptor missile can be programmed to fly in a straight line at a constant speed of v, = 1360 m/s for up to 15.0 km for the given altitudes. In your calculations, you can ignore the effects of air resistance and the height of the MFU. A hostile aircraft is flying at a constant speed of v = 580 m/s at a constant height of 6.0 km in the direction of the MFU. If the hostile aircraft is to be hit by the interceptor missile at 15.0 km from the MFU as shown in Figure 2(a), determine the horizontal distance x1 of the aircraft to the MFU when the interceptor missile has to be launched and the angle that it has to be launched. Hostile aircraft flying at constant horizontal velocity Point of collision VH = 580 m/s Flying at constant height 6.0 km 15.0 km 6.0 km Interceptor missile programmed to fly in a straight line at constant velocity v = 1360 m/s Not drawn to scale Mobile Firing Unit (MFU) has negligible height

Answer 1

a Consider the following figure: the distance X,=ditda where ---- 16.0km : *d, = √152_6? di = 13075 km * de: distance traveled by the aircroft de = Uaxt - -2=150 km Um y Let's calculate the time 150x103 For missile La Voxt t=2= To $360 m/s then, the distance da t=11.03s de=580x11.03=6397,4 = 6.40 km the distance ox Ax=dit dz=20.15 km I

is the distance traveled by the projectile as de Unext = 250x11.03 = 2457.5 m d=2076 km the horizontal distance traveled by the missile D=1152 Fol? → D=13.21 km then AX₂=d+D = 15.97 km