Because of a storm, ground controllers instruct the pilot of a plane flying at an altitude of 4 miles to make a 90° turn and climb to an altitude of 4.2 miles. The model for the path of the plane during this maneuver is                             r(t) = ⟨10 cos 10πt, 10 sin 10πt, 4 + 4t⟩, 0 ≤ t ≤ 1/ 20                                where t is the time in hours and r is the distance in miles.                              (a) Determine the speed of the plane.                                                              (b) Calculate aT and aN. Why is one of these equal to 0?

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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.