Question

PLEASE HELP ME WITH THIS PROBLEM!!!

Answer 1

Due to gravity, as the food flies across to room, it follows the path of a

parabola.

• Harold is approximately 4.018 feet tall

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

$\displaystyle a = \mathbf{-\frac{8}{121}}$

Which gives;

$\displaystyle The \ path \ of \ Jamal's \ food \ is, \ y = \mathbf{-\frac{8}{121} \cdot (x - 11)^2 + 8}$

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

$\displaystyle a = -\frac{5}{169}$

Which gives;

$\displaystyle The \ path \ of \ Dinah's \ food \ is, \ y = \mathbf{ -\frac{5}{169} \cdot (x - 13)^2 + 5}$

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;

$\displaystyle -\frac{8}{121} \cdot (x - 11)^2 + 8 = \mathbf{-\frac{5}{169} \cdot (x - 13)^2 + 5}$

$\displaystyle \frac{8}{121} \cdot (x - 11)^2-\frac{5}{169} \cdot (x - 13)^2 + 5 - 8 = 0$

$\displaystyle \frac{747}{20449} \cdot x^2 - \frac{98}{143} \cdot x -\frac{1}{99009900990} = 0$

$\displaystyle \frac{747}{20449} \cdot x^2 \approx \frac{98}{143} \cdot x$

$\displaystyle \frac{747}{20449} \cdot x \approx \frac{98}{143}$

$\displaystyle x \approx \frac{98}{143} \times \frac{20449}{747} \approx 18.76$

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;

$\displaystyle Harold's \ height \ h \approx -\frac{8}{121} \cdot (18.76 - 11)^2 + 8 \approx \mathbf{4.018}$

Harold height is approximately 4.018 feet.

Learn more about projectile motion here:

brainly.com/question/11049671