<u>Answer:</u>
<em>Resultant of two vectors having opposite direction is the difference of the two displacements having the same direction as the larger vector.
</em>
<u>Explanation:</u><u>
</u>
Resultant of two vectors is obtained by performing the vector addition operation. When the directions of both vectors are same the resultant’s direction will also be the same as the inputs. When two vectors have opposite directions, one direction will be taken positive making one vector positive and the other negative.
By performing addition of a positive and negative number we are actually taking the difference between both. Thus performing vector addition of two vectors with opposite directions is equivalent to finding the difference between the vectors. Consider a system consisting of a solid block, on which two forces F1 and F2 act in the opposite direction.
One force will be considered positive and the other is considered negative. The resultant is given by the difference of two force vectors. Displacement of the block will be in the direction of the greater force.
(1) You must find the point of equilibrium between the two forces,
<span>G * <span><span><span>MT</span><span>ms / </span></span><span>(R−x)^2 </span></span>= G * <span><span><span>ML</span><span>ms / </span></span><span>x^2
MT / (R-x)^2 = ML / x^2
So,
x = R * sqrt(ML * MT) - ML / (MT - ML)
R = is the distance between Earth and Moon.
</span></span></span>The result should be,
x = 3.83 * 10^7m
from the center of the Moon, and
R - x = 3.46*10^8 m
from the center of the Earth.
(2) As the distance from the center of the Earth is the number we found before,
d = R - x = 3.46*10^8m
The acceleration at this point is
g = G * MT / d^2
g = 3.33*10^-3 m/s^2
Using current technology, useful parallax measurements can only be found for stars up to about 340 light years (100 parsecs) away.
