Final answer:
The laser beam, straying 0.5 degrees from its path to the Moon, diverges approximately 2,088 miles from its target. Since this is greater than the Moon's radius of about 1,000 miles, the laser beam will miss the Moon.
Step-by-step explanation:
The student's question involves calculating the divergence of a laser beam that strays 0.5 degree from its path as it travels to the moon and determining if it will strike the moon. Given that the distance from the Earth to the Moon is 240,000 miles and the moon's radius is about 1,000 miles, we can solve this using trigonometry.
First, we convert the angle to radians: 0.5 degrees * (π / 180) = approximately 0.0087 radians. Then, we calculate the linear distance of the divergence (D = angle in radians * distance to Moon).
D = 0.0087 * 240,000 miles
= approximately 2,088 miles. The laser beam diverges approximately 2,088 miles from its target.
Considering the radius of the Moon is about 1,000 miles, the laser beam would miss the Moon, since the divergence distance is greater than the Moon's radius.