A projectile fired from the point (0,0) at an angle to the positive x-axis has a trajectory given by y= Cx- (1+C) (x)2 In this formula, x is the horizontal distance in meters, y is the height in meters, v is the initial velocity in meters per second, g= 9.81 m/ sec is the acceleration due to gravity, and C>0 is a constant determined by the angle of elevation A howitzer fires an artillery round with a velocity of 884 m/sec. Answer parts (a) and (b). (a) If the round must clear a hil| 234 meters high at a distance of 2496 meters in front of the howitzer, what C values are permitted in the trajectory equation? (Type your answer in interval notation. Round the final answer to the nearest thousandth as needed. Round all intermediate values to five decimal places as needed.)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.