This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the given forces and the angle between them. We are given two forces: F_1 = 7 N F_2 = 10 N The angle between these two forces is = 60^. Step 2: Apply the formula for the magnitude of the resultant force. The magnitude of the resultant force R of two forces F_1 and F_2 acting at an angle to each other is given by the law of cosines: R = sqrt(F_1^2 + F_2^2 + 2F_1F_2 ) Step 3: Substitute the values and calculate the resultant force. Substitute F_1 = 7 N, F_2 = 10 N, and = 60^ into the formula. We know that (60^) = (1)/(2). R = sqrt((7 N))^2 + (10 N)^2 + 2(7 N)(10 N) (60^) R = sqrt(49 N)^2 + 100 N^2 + 2(70 N^2)((1)/(2)) R = sqrt(49 N)^2 + 100 N^2 + 70 N^2 R = sqrt(219 N)^2 R ≈ 14.80 N The resultant of the two forces is 14.80 N. Drop the next question.