à y D MAT1005 Summer2018 : X.-Smooth Bore Cannon Ba V New Tab loads/MAT 1005%20Summer 201 8%20Final Project.pdf 8) We can calculate the horizontal range of a projectile using the following formula: v . sin2θ Theta ()is the angle at which the cannon is tilted from horizontal, and vo and g are as defined in (3). a) [I point] To see how this works, solve the following problem: the ship's cannons to test its range. The cannon was set at an angle of 21. The pirate watched the cannonball, and noted that it hit the water 850 meters away. Given that g -9.8 m/sece in metric units, what was the cannonball's velocity (in m/see) when it left the cannon (vo)? [2 points] the cannonball, making sure that the resulting distance is less than the maximum range for the cannon from (7). To do this, you will set R equal to your answer from (7), vo and g from (3), and solve for The equation you will use is below. Use the sin-1 function on your calculator and then determinewhat the angle must be. A pirate fired one of b) In our Port Royal scenario, select the angle to which the commander tilts We do not want to use an angle any larger than the one that you solved for, since we would exceed the maximum range. Pick an angle approximately 10% smaller than what you calculated for &. Using that angle, calculate R (in feet), which would represent how far away the ship must be from the wall of the fort in order for the cannonball to hit the ship. Now convert that value into nautical miles, given that 3 nautical miles is approximately 6076 yards? Helpful References: Quadratic formula calculator and solver at htp:l/www.mathwarehouse.com quadratic quadratie Smooth bore cannon ballisties: Comparison with Historic Muzzle Velocity Data AND Comparison with Historical Range Data at http://arc id.au/CannonBallistics html Non-horizontally-launched projectiles at å¥ .ml 9çºå