Due to gravity, as the food flies across to room, it follows the path of a
parabola.
Reasons:
The path followed by the food (the projectile) is a parabola
The vertex form of the equation of a projectile is; y = a·(x - h)² + k
Where;
(h, k) = The vertex
The horizontal coordinates of the vertex = Half the range
Therefore;
For Jamal, (h, k) = (11, 8)
At x = 0, y = 0, therefore;
0 = a·(0 - 11)² + 8
-121·a = 8
[tex]\displaystyle a = \mathbf{-\frac{8}{121}}[/tex]
Which gives;
[tex]\displaystyle The \ path \ of \ Jamal's \ food \ is, \ y = \mathbf{-\frac{8}{121} \cdot (x - 11)^2 + 8}[/tex]
For Dinah, we have;
y = a·(x - h)² + k
(h, k) = (13, 5)
At x = 0, y = 0, therefore;
0 = a·(0 - 13)² + 5
-169·a = 5
[tex]\displaystyle a = -\frac{5}{169}[/tex]
Which gives;
[tex]\displaystyle The \ path \ of \ Dinah's \ food \ is, \ y = \mathbf{ -\frac{5}{169} \cdot (x - 13)^2 + 5}[/tex]
At Harold's height, we have that the elevation of both food projectile are equal, therefore;
Height of Jamal's food projectile = Height of Dinah's food projectile
Which gives;
[tex]\displaystyle -\frac{8}{121} \cdot (x - 11)^2 + 8 = \mathbf{-\frac{5}{169} \cdot (x - 13)^2 + 5}[/tex]
[tex]\displaystyle \frac{8}{121} \cdot (x - 11)^2-\frac{5}{169} \cdot (x - 13)^2 + 5 - 8 = 0[/tex]
[tex]\displaystyle \frac{747}{20449} \cdot x^2 - \frac{98}{143} \cdot x -\frac{1}{99009900990} = 0[/tex]
[tex]\displaystyle \frac{747}{20449} \cdot x^2 \approx \frac{98}{143} \cdot x[/tex]
[tex]\displaystyle \frac{747}{20449} \cdot x \approx \frac{98}{143}[/tex]
[tex]\displaystyle x \approx \frac{98}{143} \times \frac{20449}{747} \approx 18.76[/tex]
x ≈ 18.76
Therefore, at Harold's height, the horizontal distance from where the food flies, x ≈ 18.76 feet.
Therefore, Harold's height is given by plugging in x ≈ 18.76 feet in either of the projectile motion as follows;
[tex]\displaystyle Harold's \ height \ h \approx -\frac{8}{121} \cdot (18.76 - 11)^2 + 8 \approx \mathbf{4.018}[/tex]
Harold height is approximately 4.018 feet.
Learn more about projectile motion here:
https://brainly.com/question/11049671
