Two ropes are attached to a tree, and forces of F⃗ 1=2.0iˆ+4.0jˆN and F⃗ 2=3.0iˆ+6.0jˆN are applied. The forces are coplanar (in
1 answer:
Answer:
We can see that the 2 forces are being applied in the same direction
So the resultant force will be larger than the given forces
Resultant force = (2i + 4j) + (3i + 6j)
R = 5i + 10j
Magnitude of the resultant force :
R² = i² + j²
R² = 25 + 100
R = =
Direction of the resultant force:
Tan Θ = Vertical component of force / Horizontal component of force
<em>Tan Θ = 10 / 5</em>
<em>Tan Θ = 2</em>
<em>Θ = Arctan (2)</em>
Θ = 63.4 degrees
Direction is 63.4 degrees in the NE direction
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Answer:
25. Approximately 8.1 meters
26. North 1.31 km, and East 2.81 km
Explanation:
25.
Notice that the displacements: 6 meters east and 5.4 south create the legs of a right angle triangle. The hypotenuse of that triangle will be the distance (d) needed to cover in order to get the ball in the hole in one putt. That is:
which can be rounded to 8.1 m.
26.
Notice that the 3.1 km at an angle of 25 degrees north of east, is the hypotenuse of a right angle triangle that has for legs the east and north components of that distance.
We can find the leg corresponding to the east displacement using the cosine function (that relates adjacent side with hypotenuse):
and we can calculate the north component using the sine function that relates the opposite side to the angle with the hypotenuse.