Final answer:
The flying squirrel will travel a total distance of 36 feet, which includes gliding from the nest to the ground, scurrying 9 feet back to the tree, and climbing 12 feet back up to the nest.
Step-by-step explanation:
The question asks us to determine the total distance a flying squirrel will travel if it glides from its nest, which is 12 feet up in a tree, to eat an acorn on the ground 9 feet away from the tree, then scurries back to the base of the tree, and finally climbs up the tree to return to its nest.
Calculating the Distance Covered by the Flying Squirrel
The total distance the flying squirrel will travel includes three parts:
The glide distance from the nest to the acorn on the ground.
The distance scurried horizontally back to the tree base.
The climb back up the tree to the nest.
Glide Distance
To calculate the glide distance, we need to find the hypotenuse of the right triangle formed by the nest's height and the horizontal distance from the tree to the acorn. We use the Pythagorean theorem:
c2 = a2 + b2
where c is the hypotenuse, a is the height of the nest (12 feet), and b is the horizontal distance to the acorn (9 feet).
c2 = 122 + 92
c = √(144 + 81)
c = √225
c = 15 feet
Scurrying and Climbing Distance
The squirrel then scurries the horizontal distance of 9 feet back to the base of the tree and climbs the vertical distance of 12 feet back to its nest.
Total Travel Distance
The total travel distance is the sum of the glide distance, the scurry back to the tree, and the climb up the tree:
Total distance = Glide distance + Scurry distance + Climb distance
Total distance = 15 feet + 9 feet + 12 feet
Total distance = 36 feet
Therefore, the total distance the squirrel will travel is 36 feet.