Answer for Day 21 Math Problem

22.02° 🎯

The angle of elevation of @jancharlest's plane 2 kilometers away horizontally from starting point is 22.02°.

Solution

The problem is under differential calculus and (plane) trigonometry. 🤯

This method has the following steps:

1. Get the height of the plane after travelling 2 kilometers away horizontally from starting position.
2. Get the first derivative of the equation of the trajectory.
3. Get the slope of the line tangent to the curve.
4. Use the arc tan function to get the angle of elevation.

First, we should get the height of the plane given the horizontal distance of 2 kilometers from initial position by substituting it to the original equation.

y = 2 - (x - 5)² / 16, where x = 2
y = 2 - (2 - 5)² / 16
y = 23/16

The angle of elevation of an object refers to how far above the horizontal line the object is pointing at. We can get the angle of elevation by using the arc sin function on the slope of the line tangent to the trajectory curve at (2, 23/16).

To get the equation of the line tangent to the trajectory, we should get the first derivative of the equation y = 2 - (x-5)² / 16. The derivative of [2 - (x - 5)² / 16] is [-(x - 5) / 8] or simply (5 - x) / 8.

To get the slope of the line tangent to the curve, we should substitute the x-value (which is 2) to the first derivative. We get (3 / 8). The slope of 3 divided by 8 means that every time the you count 3 units upwards ("rise"), you count 8 units rightwards ("run").

We can use the arc tan function to get the angle of elevation using two legs which are 3 units (the opposite side) and 8 units (the adjacent side).

arctan(3/8.544) ≈ 20.55604522° or simply 20.56°.

Winner: none 🤯

1 HIVE has been distributed to the previous days' official winners in proportion to how many days they won. 💰

• @jfang003 gets 0.693 HIVE
• @eturnerx-dbuzz gets 0.231 HIVE
• @holovision gets 0.077 HIVE

@minus-pi got the correct answer, but sadly, they had not been active on D.Buzz for the last 14 days, so they cannot be chosen as the official winner according to the official rules. 🙁

Special awardee: @minus-pi 🎖️

Because of @minus-pi's very fast and accurate response to my solution, they are awarded 1 HIVE separate from the official prizes! 😃

Mention: @ahmadmanga (@ahmadmangazap)

Let me know if there is something on this explanation you disagree with. Thanks! 😅