Question

3. (10 points) A 6.0kg object has the following two forces acting on it Pi (15 + 12)N рг"(-122 + 150) N If the object is initially at rest, determine its velocity 20s later Write the veloc ity using vectors

Answer 1

Let object at in origin F_1 vector = (15 x hat + 12 y hat) N F_2 vector = (-12 x hat + 15 y hat) N Now the angle between two forces is - F_1 vector middot F_2 vector = vert F_1 vector vert vert F_2 vector vert cos theta rightwardsdoublearrow 0 = vert F_1 vector vert vert F_2 vector vert cos theta rightwardsdoublearrow theta = pi/2 Now resultant force is in magnitude. vert F vector vert = squareroot vert F_1 vector vert^2 +vert F_2 vector vert^2 + 2 vert F_1 vector vert vert F_2 vector vert cos theta vert F vector vert = squareroot 369 + 369 = 27.16 \r\n Now Now F vector = vert F vector vert cos (83.65) x hat +vert F vector vert cos (6.35) y hat F vector = 3.00 x hat + 26.99 y hat Now F = 27.16 m dv/dt = 27.16 dv = 27.16/m dt [Because m = 6 kg] dv = 4.52 dt