What is the horizontal and vertical components of a cat's displacement when it has climbed 5 m directly up a tree?
zero horizontal and 5 vertical
To determine the horizontal and vertical components of a cat's displacement when it has climbed 5 m directly up a tree, we can use basic trigonometry.
Let's assume that the tree is straight vertical, and the cat's path is at an angle with respect to the ground. We'll call this angle θ.
The vertical component of the cat's displacement is the distance climbed up the tree, which is given as 5 m.
The horizontal component of the cat's displacement can be found using the trigonometric relationship:
cos(θ) = adjacent/hypotenuse.
In this case, the adjacent side is the horizontal component of displacement, and hypotenuse is the total displacement (the 5 m climbed up the tree). Rearranging the equation, we have:
adjacent = cos(θ) * hypotenuse.
In our case, adjacent = horizontal component of displacement, and hypotenuse = 5 m.
Therefore, the horizontal component of displacement is given by:
horizontal component = cos(θ) * 5 m.
To determine the horizontal and vertical components of a cat's displacement, we need to understand that displacement is a vector quantity that has both magnitude and direction. In this scenario, the cat has climbed directly up a tree, which means its displacement is purely vertical.
Given that the cat has climbed 5 m directly up a tree, the vertical component of its displacement will be 5 m. Since there is no horizontal movement involved, the horizontal component of its displacement will be zero.
Therefore, the horizontal component of the cat's displacement is 0 m, and the vertical component of its displacement is 5 m.