Question

PLEASE HELP ME WITH THIS PROBLEM!!!

At the elementary school, the fourth graders Jamal and Dinah are still eating lunch as they come into math class. Someone has left a book on the floor and they both trip. As they each hit the floor, the food they are carrying flies across the room directly toward Harold, who is showing off his latest dance moves.

As Jamal and Dinah watch in horror, Jamal’s cupcake and Dinah’s sandwich splat right on top of Harold’s head! Jamal’s cupcake flies on a path that would have landed on the floor 22 feet away from him if it had not hit Harold. Dinah’s sandwich flies on a path that would have landed on the floor 26 feet away from her if it had not hit Harold. Jamal’s cupcake flies 8 feet high, while Dinah’s sandwich reaches a height of 5 feet before hitting Harold.



How tall is Harold? Once you have the equations, you may use Desmos to help find the answer.



This question uses a numeric answer. Type in just the number part answer (no letters!) and round to 2 decimals.

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:

https://brainly.com/question/11049671