Larry likes skeet shooting, where a clay disc is shot into the air, and the participant tries to shoot it as it flies through the air. The discs are released from a firing mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120 m on a parabolic path. On avergae, the skeet hits a height of 37.5 m after travelling a horizontal distance of 45 m.
a. Determine the equation of a function, in standard form, that represents the flight of the clay disc. Leave valuses in fractions.
b. Determine the average maximum height of the skeet by completing the square.
7 years ago
Answered By Alireza R
From the question, it is understood that the path that disc flies is parabolic.
General parabolic equation is Ax2+Bx+C=Y. To determine the equation we need three points on the parabola.
The points are given inthe question as follows:
1- If we set the origin on the location of the gun for the first point, we have X=0 and Y=0. The equation will be:
A(0)2+B(0)+C=0
$\therefore$∴ C=0
2- It isgiven that the horizontal distance that the disc is shoot is 120m. This is the second point, and since the disc is fallen on the ground, X=120 and Y=0. The equation will be like this:
A(120)2+B(120)=0
$\therefore$∴ 120A=-B or B=-120A
We have to unknowns, A and B. To solve the equation, we need another point.
3- the third point is the skeet hits a height of 37.5 m after travelling a horizontal distance of 45 m, at this point, X=45 and Y=37.5. The equation will be written as follows:
A(45)2+B(45)=37.5
In above equation, B is replaced with -120A and the values foa A and B are calculated as follows:
A=-1/90
B=4/3
and the parabolic equation is:
Y=-X2/90 + 4X/3.
To answer the second point of the question, We calculate the the corresponding Y when X=-B/(2A).
-B/2A=60, X=60, Y=40. This is the maximum height of the object.
The simple method to calculate maximum height is to calculate height when the disc is half way through (60m).
Attached Graph:
7 years ago
Answered By Alireza R
From the question, it is understood that the path that disc flies is parabolic.
General parabolic equation is Ax2+Bx+C=Y. To determine the equation we need three points on the parabola.
The points are given inthe question as follows:
1- If we set the origin on the location of the gun for the first point, we have X=0 and Y=0. The equation will be:
A(0)2+B(0)+C=0
$\therefore$∴ C=0
2- It isgiven that the horizontal distance that the disc is shoot is 120m. This is the second point, and since the disc is fallen on the ground, X=120 and Y=0. The equation will be like this:
A(120)2+B(120)=0
$\therefore$∴ 120A=-B or B=-120A
We have to unknowns, A and B. To solve the equation, we need another point.
3- the third point is the skeet hits a height of 37.5 m after travelling a horizontal distance of 45 m, at this point, X=45 and Y=37.5. The equation will be written as follows:
A(45)2+B(45)=37.5
In above equation, B is replaced with -120A and the values foa A and B are calculated as follows:
A=-1/90
B=4/3
and the parabolic equation is:
Y=-X2/90 + 4X/3.
To answer the second point of the question, We calculate the the corresponding Y when X=-B/(2A).
-B/2A=60, X=60, Y=40. This is the maximum height of the object.
The simple method to calculate maximum height is to calculate height when the disc is half way through (60m).
Attached Graph: