(a) Plot a scatter diagram of the data in thetable below. Let x be the weight in
ID: 3089312 • Letter: #
Question
(a) Plot a scatter diagram of the data in thetable below. Let x be the weight in kilograms and let y be thevelocity in meters per second.
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
(b) Determine which type of function would fit thisdata the best: linear or quadratic. Use a graphing utility to findthe function of best fit. Are the results reasonable?
(c) Based on velocity, we can determine howhigh a projectile will travel before it begins to come backdown. If a cannon is fired at an angle of 45° to thehorizontal, then the function for the height of the projectile isgiven by;
s(t) = -16t² + (2/2) v0t +s0
where v0 is the velocity at which the shell leaves the cannon(initial velocity), and s0 is the initial height of the nose of thecannon ( because cannons are not very long, we may assume that thenose and the firing pin at the back are at the same height forsimplicity). Graph the function s=s(t) for eachof the guns described in the table. Which gun would be thebest for anti-aircraft if the gun were sitting on theground? Which would be the best to have mounted on a hilltopor on the top of a tall building? If the guns were on theturret of a ship, which would be the most effective?
Use the s0 given below for height on ground, height on hill ortall building, and height on the turret of a ship.
s0 =0 s0 =200m s0 = 30m
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
Explanation / Answer
a) using a program like excel put the points in a data tablethen create a scatter plot graph. b) Projectile problems are always parabolic so this is a quadraticequation. I don't know which graphing utility you can use tofind the best fit line but excel might work. c) For this given the equation use a graphing calculator to graphthe equation and using the table and given values for so plug theminto the equation. since the gun is anti aircraft, the mosteffective one will have the highest height s(t).
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