Question

Balcony-sized solar cookers have been designed for families living in India. The top of a dish has a diameter of 1600 mm. The sun’s rays reflect off the parabolic mirror toward the "cooker," which is placed 320 mm from the vertex of the mirror. What is the depth of the cooker?

Answer 1

Answer: 500mm

Explanation:

The vertex of the parabolic mirror is the origin of the coordinate plane, so the parabola will take the standard for y2=4px, where p>0. The cooker, which is the focus, is 320 mm away from the vertex of the mirror. Thus, we have p=320, which we can use to solve for the equation of the parabola.

y2y2y2=4px=4(320)x=1280x.

The dish extends 16002=800 mm on either side of the origin. We can substitute 800 for y into the equation above to find the depth of the cooker.

y2(800)2y=1280x=1280y=500.

Therefore the cooker is 500 mm deep.

Answer 2

The depth of the cooker is 320 mm.

To find the depth (y) of the cooker in a parabolic solar cooker, use the equation of a parabola;

y = ax²

Where; (a) is a constant.

1. Determine (a):

a = y/x² = 320mm / (800mm)² = 5 × 10^-4 mm^-1

2. Use (a) to find the depth (y)

when (x) is the distance from the vertex to the rim (800 mm):

y = ax²

y = (5 × 10^-4(mm^-1) • (800mm)²

y = 320mm

Therefore, the depth of the cooker is 320 mm.