An insect walks 50 cm in a straight line along a wall. if its horizontal displacement is 25 cm,?
calculate its vertical displacement.
X^2 + Y^2 = r^2
X = 25 cm
Y = Ver. Displacement
r = 50 cm = Hypotenuse.
Solve for Y.
To find the vertical displacement of the insect, we can use the Pythagorean theorem.
According to the theorem, the square of the hypotenuse (the straight-line distance walked by the insect) is equal to the sum of the squares of the other two sides (vertical and horizontal displacements).
Let's denote the vertical displacement as "y" and the horizontal displacement as "x".
We know that the horizontal displacement, x, is 25 cm.
Using the Pythagorean theorem, we can set up the following equation:
c^2 = a^2 + b^2
Where c is the hypotenuse (50 cm) and a and b are the vertical and horizontal displacements, respectively.
Substituting the values into the equation, we get:
50^2 = 25^2 + y^2
2500 = 625 + y^2
Subtracting 625 from both sides, we have:
y^2 = 2500 - 625
y^2 = 1875
Taking the square root of both sides, we find:
y = √1875
Using a calculator, we can find the square root of 1875 ≈ 43.3.
Therefore, the vertical displacement of the insect is approximately 43.3 cm.
To calculate the vertical displacement of the insect, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we can consider the horizontal displacement as one side of the triangle and the vertical displacement as the other side. The hypotenuse would be the insect's actual displacement, which is 50 cm.
Now, let's calculate the vertical displacement:
1. Apply the Pythagorean theorem:
horizontal displacement squared + vertical displacement squared = insect's displacement squared
25 cm squared + vertical displacement squared = 50 cm squared
625 + vertical displacement squared = 2500
2. Solve for vertical displacement:
vertical displacement squared = 2500 - 625
vertical displacement squared = 1875
vertical displacement = square root of 1875
vertical displacement ≈ 43.30 cm
Therefore, the vertical displacement of the insect is approximately 43.30 cm.