Hannah has a solid wooden globe of radius 1 metre. Starting at the point P at 60◦ N, 0◦ E on the surface of the globe, Flik the termite burrows d metres straight down into the ground (of the globe) to the point F. Next, Flik crawls back up to the surface of the globe. Finally, Andy saws the globe all the way through the parallel at 45◦ N, and the saw passes through point F. Determine with justification the exact value of d. Include a labelled diagram.
A) 0.5 metres
B) 1 metre
C) 1.5 metres
D) 2 metres

To determine the value of d, first calculate the distance Flik burrows, then find the horizontal and vertical components after the globe is sawn through. The correct answer is A) 0.5 meters.

Explanation:

To determine the exact value of d:

First, find the distance Flik burrows straight down. Using the Pythagorean theorem on a triangle with sides of 1 meter, the radius, and d meters, you get d = √(1^2 - (1/√2)^2) = 1/√2 = 0.707 meters.
Next, since Andy saws the globe at 45° N, forming a right triangle, the vertical component is 1 - d, and the horizontal component is d/√2 = 0.5 meters.
Therefore, the exact value of d is 0.707 meters, which falls between the given options, closest to 0.5 meters, so the correct answer is A) 0.5 meters.