Two forces whose resultant vector is 100newtons,are perpendicular to each other.if one of them makes an angle of 60degrees with the resultant,calculate its magnitude
To solve this problem, we can use vector addition and the concept of trigonometry.
Let's call the magnitude of the first force F1 and the magnitude of the second force F2.
Since the two forces are perpendicular to each other, their vector sum (resultant) can be found using the Pythagorean theorem:
Resultant magnitude^2 = F1^2 + F2^2
Given that the resultant magnitude is 100 newtons, we can write the equation as:
100^2 = F1^2 + F2^2
Simplifying the equation, we have:
10000 = F1^2 + F2^2 -----(1)
Now, let's consider the angle between one of the forces (F1) and the resultant. We are told that this angle is 60 degrees.
Using trigonometry, we can relate the magnitudes of the forces and the angle with the cosine function:
F1 = Resultant magnitude * cosine(angle)
Substituting the given values, we have:
F1 = 100 * cosine(60)
To calculate the value of cosine(60), we can use a calculator or refer to a trigonometric table. The cosine of 60 degrees is 0.5.
So, we can calculate F1 as:
F1 = 100 * 0.5
= 50 newtons
Now, we can substitute F1 = 50 in equation (1) to solve for F2:
10000 = 50^2 + F2^2
10000 = 2500 + F2^2
F2^2 = 10000 - 2500
= 7500
Taking the square root of both sides, we have:
F2 = √7500
≈ 86.60 newtons
Therefore, the magnitude of the second force is approximately 86.60 newtons.