RELATED RATES PLAYLIST: https://goo.gl/85bbsG
__________
In this video you will learn how to find the Maximum Rate of Change of the angle between the observer and the airplane, given the speed of the airplane and its altitude relative to the ground.
A spectator at an air show is trying to follow the flight of a jet. The jet follows a straight path in front of the observer at 540 miles per hour. At its closest approach, the jet passes 600 feet in front of the person. Find the maximum rate of change of the angle between the spectator's line of sight and a line perpendicular to the flight path, as the jet flies by.
0:40 Drawing & Understanding picture with given Info
2:44 Converting from miles per hour to feet per second
3:40 Understanding what needs to be solved for - max θ'(t)
4:32 Finding equation involving angle θ(t)
5:07 Differentiating the found equation implicitly
5:36 Rewriting equation that solves for θ'(t)
5:55 Solving for θ'(t) by plugging in known quantities into equation
6:22 Understanding how to find the maximum value for θ'(t)
Related Videos to this topic:
Related Rates: Kite problem
https://youtu.be/JkKr1hDYDBQ
Related Rates: Curve problem
https://youtu.be/HEzg857kY3U
Related Rates: Boat problem
https://youtu.be/GU10f0HKFTg
Related Rates: Pulley & Rope problem
https://youtu.be/qgBzwrb5AcQ
Related Rates: Shadow Problem {lamp post; finding shadow LENGTH rate of change s'(t)}
https://youtu.be/A_IA-X44e2w
Related Rates: Cone Problem - finding h'(t)
https://youtu.be/QLYwZJAFlfE
Related Rates: Complex Trigonometry Problem {θ'(t)=-θ1'(t)-θ2'(t)}
https://youtu.be/h0gZo3FbV6Y
Related Rates: Sliding Ladder Problem - finding x'(t)
https://youtu.be/BQGjhejoUNI
Related Rates: Oil Spill Problem - finding r'(t)
https://youtu.be/MLHC96qqbQ0
Related Rates: 3-Variable Problem - 2 approaching cars, finding d'(t)
https://youtu.be/-xduJ7ybPX4
Related Rates: Sphere Problem {finding r when S'(t)=r'(t)}
https://youtu.be/J83SK31jQD0
Related Rates: Balloon Problem - finding S'(t)
https://youtu.be/vtytsSlSRGc
______________________
CALCULUS PLAYLIST: https://goo.gl/sw5cj5