Math mini-contest problem for Day 21 on D.Buzz for February 2021 😎
Math Problem for Day 21 😎
@jancharlest threw a paper airplane whose trajectory is y = 2 - (x-5)² / 16.
y = kilometers (km) above sea level
x = horizontal distance in km from @jancharlest
After flying for 2 km horizontally, what is the angle of elevation of the plane?
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0.000
My guess this time is 54.29 degrees. My work will be in the following comment.
Substitute x=2 in the above equation, we get y=23/16 km for the height.
Now the distance direct line distance of x^2+y^2 = z^2 gives z=2.463.
The angle I calculated is arcsin(x/z) which gives me 54.29 degrees (converted the radians).
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STOPCheck out the last post from @hivebuzz:
slope is first deviation:
y' = -(x-5) / 8=>y'(2) = 3/8. This corresponds to 20.56 degreeedit: sorry for the flag initially, I hit the wrong button :D
Guess:
35.7067 degNot sure what angle of elevation is. If it's the slope of the trajectory then the others have answered. I'll hedge a guess it's the angle from where the plane was thrown!
Subst in
x=2givesy = ~1.4375. The vector(2, 1.4375)has angle35.7067 deg.Posted via D.Buzz
Answer for Day 21 Math Problem
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:
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. 💰
@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)
Hey @savvyplayer, me again, I hope you don't mind :D
I'm fully with you up to to the slope of 3/8, but I believe the angle is then calculated with arctan(opposite/adjacent). Arcsin would need opposite over hypotenuse. Arctan(3/8) = 20.56
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Have an upvote prize for winning. Congrats.
Thanks a lot @eturnerx, highly appreciated :D
Posted via D.Buzz
Thanks for correcting my solution! 😃 I have made an obvious mistake. 😅 I have sent you 1 HIVE as reward, separate from the prizes normally sent to winners who had been active D.Buzz members! 😊