Answer:
Magnitude of C= 
Angle=arctan(Ay+By/Ax+Bx)
Explanation:
Let
A = Axi + Ayj
B = Bxi + Byj
where i and j are unit vectors in the direction of x and y axes respectively.
C=A+B
C = (Ax + Bx)i + (Ay + By)j
The magnitude of vector C can be calculated by adding the square of magnitude of its componets and then taking sqaure root.
Magnitude of C= 
And the angle will be
Angle=arctan(Ay+By/Ax+Bx)
Answer:
The period of the system of ladder and woman, T = 2.5 seconds
Explanation:
Mass of the ladder, 
Mass of the artiste, 
Length of the ladder, L = 42.0 kg
The total moment of inertia can be calculated using the equation:

D = L/2 = 3/2
D = 1.5 m
The frequency of the system of ladder and woman follows that of a physical pendulum which can be given by the equation:

The period of the system of ladder and woman is given by:
T = 1/f
T = 1/0.4
T = 2.5 seconds
Answer:
Option B
Explanation:
Option A is the wrong answer because the horizontal vector is in the opposite direction.
Option C is the wrong answer as the horizontal vector is in the opposite direction and all the vectors are connected head to tail [of the arrows] [Triangle law of vector addition]
Option D is the wrong answer as the horizontal vector is in the opposite direction.
Answer: 2.85 N.s
Explanation: Impulse is the product of force and time or expressed in the following formula:
J = F x t
= 475 N x 0.006 s
= 2.85 N.s