Assumptions

This section simplifies the original problem and helps in developing the theoretical models by filling in the missing information for the physical system. The assumptions refine the scope by providing more detail.

twoDMotion: The projectile motion is two-dimensional (2D). (RefBy: GD:velVec and GD:posVec.)

cartSyst: A Cartesian coordinate system is used (from A:neglectCurv). (RefBy: GD:velVec and GD:posVec.)

yAxisGravity: The direction of the \(y\)-axis is directed opposite to gravity. (RefBy: IM:calOfLandingDist, IM:calOfLandingTime, and A:accelYGravity.)

launchOrigin: The launcher is coincident with the origin. (RefBy: IM:calOfLandingDist and IM:calOfLandingTime.)

targetXAxis: The target lies on the \(x\)-axis (from A:neglectCurv). (RefBy: IM:calOfLandingTime.)

posXDirection: The positive \(x\)-direction is from the launcher to the target. (RefBy: IM:offsetIM, IM:messageIM, IM:calOfLandingDist, and IM:calOfLandingTime.)

constAccel: The acceleration is constant (from A:accelXZero, A:accelYGravity, A:neglectDrag, and A:freeFlight). (RefBy: GD:velVec and GD:posVec.)

accelXZero: The acceleration in the \(x\)-direction is zero. (RefBy: IM:calOfLandingDist and A:constAccel.)

accelYGravity: The acceleration in the \(y\)-direction is the acceleration due to gravity (from A:yAxisGravity). (RefBy: IM:calOfLandingTime and A:constAccel.)

neglectDrag: Air drag is neglected. (RefBy: A:constAccel.)

pointMass: The size and shape of the projectile are negligible, so that it can be modelled as a point mass. (RefBy: GD:rectVel and GD:rectPos.)

freeFlight: The flight is free; there are no collisions during the trajectory of the projectile. (RefBy: A:constAccel.)

neglectCurv: The distance is small enough that the curvature of the celestial body can be neglected. (RefBy: A:targetXAxis and A:cartSyst.)

timeStartZero: Time starts at zero. (RefBy: GD:velVec, GD:rectVel, GD:rectPos, GD:posVec, and IM:calOfLandingTime.)

gravAccelValue: The acceleration due to gravity is assumed to have the value provided in the section for Values of Auxiliary Constants. (RefBy: IM:calOfLandingDist and IM:calOfLandingTime.)