Answer:
78 m
Explanation:
The cannonball is fired horizontally, at a tangent to the Earth's surface. Therefore, this trajectory forms a right angle (90 degree angle) with the radius line from the Earth's center to the ship. Treating the Earth as a perfect sphere, the radius is the same at all points along the Earth's surface. Therefore, we can use Pythagorean theorem to find the vertical distance between the cannonball and the Earth.
[tex]\Large \text {$ a^2+b^2=c^2 $}\\\\\Large \text {$ (6370-x)^2+(31.6)^2=(6370)^2 $}\\\\\Large \text {$ (6370-x)^2=(6370)^2-(31.6)^2 $}\\\\\Large \text {$ 6370-x=\sqrt{(6370)^2-(31.6)^2} $}\\\\\Large \text {$ 6370-x\approx 6369.922 $}\\\\\Large \text {$ x\approx 0.078 $}[/tex]
The cannonball is about 0.078 km above the Earth's surface, or 78 meters.
