Aircraft Liftoff 3D#

A hot air balloon takes off at $$A$$ and climbs at a steady angle, $$\theta\_{1} = {{params.angle}}^{\circ}$$ in the y-z plane at a speed of 5 $$km/h$$. The hot air balloon is watched by two observers $$O$$. Calculate the following values as the balloon passes point $$B$$, $$x =$$ 490 $$m$$ and $$z =$$ 318 $$m$$.

Part 1#

Calculate $$\dot{R}$$.

Part 2#

Calculate $$\dot{\theta}$$.

Calculate $$\dot{\phi}$$.