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:
Explanation:
Solve using the quadratic formula.
<h2>5.3 km</h2>
Explanation:
This question involves continuous displacement in various directions. When it becomes difficult to imagine, vector analysis becomes handy.
Let us denote each of the individual displacements by a vector. Consider the unit vectors as the unit vectors in the direction of East and North respectively.
By simple calculations, we can derive the unit vectors in the directions North,
South of West and
North of West respectively.
So Total displacement vector = Sum of individual displacement vectors.
Displacement vector =
Magnitude of Displacement =
∴ Total displacement =