Two trees have perfectly straight trunks and are both growing perpendicular to the flat horizontal ground beneath them. The sides of the trunks that face each other are separated by 1.2 m. A frisky squirrel makes three jumps in rapid succession. First, he leaps from the foot of one tree to a spot that is 0.8 m above the ground on the other tree. Then, he jumps back to the first tree, landing on it at a spot that is 1.5 m above the ground. Finally, he leaps to the other tree, now landing at a spot that is 2.3 m above the ground. What is the magnitude of the squirrel's displacement?
I presume the question is trying to get you to calculate the distance travelled by the squirrel. In which case start with a diagram.
My answer to the question, would, however, be 2.3 m vertically from the ground as the question does not state the displacement being asked for.
To find the magnitude of the squirrel's displacement, we need to determine the distance between the starting point and the ending point of its path.
Let's analyze the situation step by step:
Step 1: The squirrel jumps from the foot of one tree to a spot that is 0.8 m above the ground on the other tree.
Since both trees have straight trunks and are growing perpendicular to the ground, we can treat this as a two-dimensional problem. The squirrel's first jump can be considered as a horizontal displacement, moving from one tree to the other.
The horizontal distance between the two trees is given as 1.2 m. Therefore, the squirrel's displacement in this step is 1.2 m.
Step 2: The squirrel jumps back to the first tree, landing on it at a spot that is 1.5 m above the ground.
In this step, the squirrel moves vertically from the other tree back to the first tree. We can calculate the vertical displacement by subtracting the heights of the landing spots on each tree.
The height difference between the landing spots is 1.5 m - 0.8 m = 0.7 m.
Step 3: Finally, the squirrel leaps from the first tree to the other tree, now landing at a spot that is 2.3 m above the ground.
Similar to step 2, we calculate the vertical displacement by subtracting the heights of the landing spots on each tree.
The height difference between the landing spots is 2.3 m - 1.5 m = 0.8 m.
Now, we have the horizontal displacement, 1.2 m, and the vertical displacements, 0.7 m and 0.8 m.
To find the magnitude of the squirrel's displacement, we can use the Pythagorean theorem. The displacement is the hypotenuse of a right triangle, where the horizontal and vertical displacements are the two legs.
Using the Pythagorean theorem:
Displacement = √(horizontal displacement^2 + vertical displacement^2)
Displacement = √(1.2^2 + 0.7^2 + 0.8^2)
Displacement = √(1.44 + 0.49 + 0.64)
Displacement = √2.57
Displacement ≈ 1.60 m
Therefore, the magnitude of the squirrel's displacement is approximately 1.60 meters.