Teenagers
1 answer:
You might be interested in
Answer:
162 km
Explanation:
A diagram can be helpful.
Using the law of cosines, we can find the magnitude of the distance (c) to satisfy ...
c^2 = a^2 +b^2 -2ab·cos(C)
where C is the internal angle of the triangle of vectors and resultant. Its value is ...
180° -39.8° -59.9° = 80.3°
Filling in a=76 and b=156, we get ...
c^2 = 76^2 +156^2 -2·76·156·cos(80.3°) ≈ 26116.78
c ≈ √26116.78 ≈ 161.607
The magnitude of the total displacement is about 162 km.
_____
Please note that in the attached diagram North is to the right and East is up. That alteration of directions does not change the angles or the magnitude of the result.
The work done by the rope on the box is equal to:
where F is the force applied by the rope, d the distance covered by the box and
is the angle between the direction of the force and of the displacement.
Using the data of the problem:
, 
and 
, we find the work:
where F is the force applied by the rope, d the distance covered by the box and
Using the data of the problem: