Due to gravity, as the food flies across to room, it follows the path of a
parabola.
- Harold is approximately <u>4.018 feet tall</u>
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
Which gives;
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
Which gives;
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;
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 <em>x </em>≈ 18.76 feet in either of the projectile motion as follows;
Harold height is approximately <u>4.018 feet</u>.
Learn more about projectile motion here: