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Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.



Welcome soldier,

It is in the heart of World War 2 and imagine yourself hunkered down in a trench line with your squad, and that there is also an enemy squad nearby opposing your movement. Both squads appear evenly matched, and there has been a stalemate for hours. There is a mortar kit which includes a rudimentary range finder, but unfortunately for your squad, no one knows how to operate it properly; however, at this point, attempting to use it is becoming your only viable option. You hop onto the radio with your superior who puts you through to an artillery specialist...

"Listen up, lieutenant. Do you have a pen, paper, and your slide rule? Good, you will need those to do your calculations. Your range finder is going to provide you with a horizontal distance between you and the enemy unit. The stereoscope will need to be focused for an accurate reading. I recommend that you don't get spotted using it just yet. You will then need to use that range and also the exit velocity of your mortar round to determine what angle you will need to use to successfully land your shot. I will send you the info for the M2 mortar and the physics behind it right away, but when you start firing, I want you to radio me the angle and flight time so that I know that your calculations are at least somewhat accurate. Good luck, soldier. Now give 'em hell!"

M2 Mortar Round Specifications:

Shell Weight 1.4kg
Caliber 60mm
Elevation 40° - 85°
Rate of Fire 18 rounds/minute
Max Range 1.8km
Initial Velocity 158 meters/second


Physics Formulas:

Θ = (arcsin((R*g)/v^2))/2

t = (2*v*sinΘ)/g

R = Range (in meters)
g = Acceleration due to gravity (9.8 meters/second^2)
v = Initial velocity (in meters/second)
Θ = Mortar angle/elevation (in radians)
t = Time of Flight (in seconds)

Note that the potential trajectories come in pairs where there are two different angles that can achieve the same range. For example, if the calculation produces an elevation of 10°, then 80° (90° - 10°) will also work.

I derived the formula for theta, but more information is available in this free text. I recommend reading through the short section on Projectile Motion completely if you have the time, specifically the sub-section Time of Flight, Trajectory, and Range.)

In this problem, we can assume zero air resistance, and that the mortar and the target have the same vertical displacement (they are in-line horizontally).
Line 1: A string which includes the range in meters. Extraneous characters represent the rangefinder being out of focus, but the digits included are the range needed for the problem.
Line 1: The value of the angle rounded to the tenth of a degree.
Line 2: The time of flight rounded to the nearest tenth of a second.

If the target is out of range, simply print OUT OF RANGE.
There are a couple constraints embedded in the problem statement.
84.3 degrees
32.1 seconds

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