TASK$-12($Cartesian Coordinates. Curvilinear motion: Normal & Tangential Coordinates$)$

At a certain point of landing of the spacecraft on the Moon, the total velocity $"v"$ of the spacecraft can be represented by two components in the Cartesian coordinate system: $vx=-45\frac{m}{s},vy=-3\frac{m}{s}.$

For this instant CALCULATE the radius of curvature $R$ of the path $($also often called as instantaneous radius of rotation$).$

Assume, that the only force, acting on the spacecfaft $($at the instant shown$),$ is the gravitational force of the Moon with its gravitational acceleration $g=1\mathrm{.}6\frac{m}{s^2}.$

Figure$-12$: $2$D trajectory of the spacecraft, landing on the Moon.