Multiple Round Simultaneous Impact (MRSI) is a term used in artillery which desc
ID: 1957271 • Letter: M
Question
Multiple Round Simultaneous Impact (MRSI) is a term used in artillery which describes the process of firing several large shells at a target with the aim of getting them to land at exactly the same time (it stops people running to hide after the first shell lands). The technique works because shells fired at different elevations take different times to reach the target. Shells that follow high trajectories take longer to land than shells that follow shallow trajectories.
Three shells are to be fired and they need to land simultaneously. The first shell will be fired at an elevation of 60° from the horizontal, followed by shell 2 at 45°, and shell 3 at 30°. Calculate the required muzzle velocity of each shell and the time between shells that would result in them landing simultaneously.
The target is 15km away and 400m higher than current position.
Explanation / Answer
Two things have to happen for each round: it has to go 15,000m and also needs to be 400m up at the same time. Horizontal component of the velocity is constant. We can use distance equals rate times time. V cos(theta)*t = 15 000 dividing by V cos(theta) yields t = 15 000/Vcos(theta) EQN TIME we also have change in y = V sin(theta)*t - (1/2)gt^2 400 = V sin(theta)*t - (1/2)gt^2 substituting in t from EQN TIME gives us 400 = V sin(theta){15 000/Vcos(theta)} - (1/2)g {15 000/Vcos(theta)}^2 some variables cancel 400 = 15 000tan(theta) - (1/2) g {15 000/Vcos(theta)}^2 get V all by itself on one side of the equals sign in the numerator to the first power. 15000tan(theta)-400 = 1103625000/[V^2 cos(theta)^2] V^2 = 1103625000/[cos(theta)^2]/{15000tan(theta)-400} V = SQRT(1103625000/[cos(theta)^2]/{15000tan(theta)-400}) time = 15 000/Vcos(theta) 60 deg V = 415m/s t = 72.2 s 45 deg V = 389 m/s t = 54.6s 30 deg V = 422m/s t = 41s 60 deg round shoot immediately 45 deg round wait 17.66 s 30 deg round wait 31.18 s
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