The velocity of the projectile depends upon several factors, in particular, weight of the ammunition.
i) Draw the scatter diagram of data in table below. Consider x be the weight in kilograms and consider y be velocity in meters persecond.
|
Type
|
|
Weight
|
|
Initial Velocity
|
|
|
(kg)
|
|
(m/sec)
|
|
MG 17
|
|
10.2
|
|
905
|
|
MG 131
|
|
19.7
|
|
710
|
|
MG 151
|
|
41.5
|
|
850
|
|
MG 151/20
|
|
42.3
|
|
695
|
|
MG /FF
|
|
35.7
|
|
575
|
|
MK 103
|
|
145
|
|
860
|
|
MK 108
|
|
58
|
|
520
|
|
WGr 21
|
|
111
|
|
315
|
ii) Determine which kind of function would fit data best: linear orquadratic. Use graphing utility to compute function of bestfit. Are results reasonable?
iii) Based on velocity, we can find how high the projectile will travel before it starts to come back down. If the cannon is fired at the angle of 45° to horizontal, then function for height of projectile is provided by;
s(t) = -16t² + √ (2/2) v0t +s0
where v0 is velocity at which shell leaves cannon(initial velocity), and s0 is initial height of nose of cannon (because cannons are not very long, we may suppose that nose and firing pin at back are at same height for simplicity). Graph function s=s(t) for each of guns described in table. Which gun would be the best for anti-aircraft if gun were sitting on ground? Which would be to have mounted on the hill top or on top of tall building? If guns were on the turret of ship, which would be most effective?
Use s0 provided below for height on ground, height on hill ortall building, and height on turret of ship.
s0 =0 s0 =200m s0 = 30m