Answer:
The answer is E) 6.7m at an angle 63° north of east
Explanation:
We begin by writing out our given vectors A,B and C in their respective rectangular Cartesian coordinate form. which are given as A=8i, B=6j and C= -5j (negative because it points towards west which is towards the left which is taken as the negative direction).Now we simply add all three to obtain our final vector given by,

In the last step we just added the like components. Now we will have to calculate the magnitude and angle of V(with respect of the east direction), which is given by,

the angle alpha is always calculated with respect to the horizontal positive axis, and since both components of the vector are positive the vector lies in the first quadrant. Hence the 63° angle north of east is justified. The term north of east means the angle formed in moving from east towards the north that is from the positive horizontal axis to the positive vertical axis.
To solve this problem it is necessary to apply the concepts related to the relationship between tangential velocity and centripetal velocity, as well as the kinematic equations of angular motion. By definition we know that the direction of centripetal acceleration is perpendicular to the direction of tangential velocity, therefore:

Where,
V = the linear speed
r = Radius
Angular speed
The angular speed is given by


Replacing at our first equation we have that the centripetal acceleration would be



To transform it into multiples of the earth's gravity which is given as
the equivalent of 1g.


PART B) Now the linear speed would be subject to:



Therefore the linear speed of a point on its edge is 51.05m/s
Answer:
<h2>117.6 J</h2>
Explanation:
The gravitational potential energy of a body can be found by using the formula
GPE = mgh
where
m is the mass
h is the height
g is the acceleration due to gravity which is 9.8 m/s²
From the question we have
GPE = 6 × 9.8 × 2
We have the final answer as
<h3>117.6 J</h3>
Hope this helps you
Answer;
Q = 359.2-J
Explanation;
Given that;
Constants for mercury at 1 atm
Heat capacity of Hg(l) is 28.0 J/(mol*K)
melting point is 234.32 K
Enthalpy of fusion is 2.29 kJ/mol
17.7-g Hg / 200.6g/mol = 0.0882 mol Hg;
°C + 273 = 298 K;
2.29-kJ/mol = 2290-J/mol
Q = (m x ΔT x Cp) + (m x Hf)
Q = 0.0882-mol x (298 - 234.32) x 28.0-J/mol*K) + (0.0882-mol x 2290-J/mol)
Q = 157.26-J + 201.978-J
Q = 359.2-J
Q=359-J (3 sig fig allowed due to 17.7-g given in problem)