A jogger travels a route that has two parts. The first is a displacement A of 2.30 km due south, and the second involves a displacement B that points due east. The resultant displacement A + B has a magnitude of 3.63 km. What is the magnitude of B?
3.63^2-2.3^2=B^2
solve for B
To find the magnitude of B, we need to use the Pythagorean theorem. According to the theorem, the square of the magnitude of the resultant displacement is equal to the sum of the squares of the magnitudes of the individual displacements:
(A + B)^2 = A^2 + B^2
Given that the magnitude of the resultant displacement (A + B) is 3.63 km, and the magnitude of displacement A is 2.30 km, we can substitute these values into the equation:
(3.63)^2 = (2.30)^2 + B^2
Expanding the equation:
13.1769 = 5.29 + B^2
Simplifying:
B^2 = 13.1769 - 5.29
B^2 = 7.8869
Taking the square root of both sides to solve for B:
B = √(7.8869)
B ≈ 2.81 km
Therefore, the magnitude of B is approximately 2.81 km.
To find the magnitude of B, you 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 problem, A and B form a right triangle, with A as the southward side and B as the eastward side.
Given that the magnitude of A + B is 3.63 km, we can find the magnitude of B by subtracting the magnitude of A from the magnitude of A + B:
Magnitude of B = Magnitude of A + B - Magnitude of A
Magnitude of B = 3.63 km - 2.30 km
Magnitude of B = 1.33 km
So, the magnitude of B is 1.33 km.