Please solve all those problems.

Type WEIGHT INITIAL VELOCITY (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

MGr 21. 111 315

a) Plot a scatter diagram of the data in the table below. Let x be the weight in kilograms and let y be the velocity in meters per second.

(b) Determine which type of function would fit this data the best: linear or quadratic. Use a graphing utility to find the function of best fit. Are the results reasonable?

(c) Based on velocity, we can determine how high a projectile will travel before it begins to come back down. If a cannon is fired at an angle of 45 to the horizon-tal, then the function for the height of the projectile v2 is given by s (t) = -16t+ 2 vot + so, where vo is the velocity at which the shell leaves the cannon (initial velocity), and so is the initial height of the nose of the cannon (because cannons are not very long, we may assume that the nose and the firing pin at the back are at the same height for simplicity). Graph the function s = st) for each of the guns described in the table. Which gun would be the best for anti-aircraft if the gun were sitting on the ground? Which would be the best to have mounted on a hilltop or on the top of a tall building? If the guns were on the turret of a ship, which would be the most effective?