Answer:
50.00N
Explanation:
The diagram for this question has been drawn and attached to this response.
As shown in the diagram,
Let the first vector be A
Let the second vector be B
Let the resultant vector be R
R = A + B (The resultant is the vector sum of the two vectors)
One of the vectors (B in this case) makes an angle of 60 with the resultant R.
Since the two vectors are perpendicular (90 degrees) to each other, then, the second vector A makes an angle 30 degrees with the resultant vector R
Now
Let's resolve the vectors A, B and R into the x and y components
R = (100 cos 60°) i + (100 sin 60°) j
A = 0 i + A j
B = B i + 0 j
Remember that:
R = A + B
Now substitute the values of R, A and B as follows;
(100 cos 60°) i + (100 sin 60°) j = 0 i + A j + B i + 0 j
Collect like terms
(100 cos 60°) i + (100 sin 60°) j = (0 + B)i + (A + 0) j
(100 cos 60°) i + (100 sin 60°) j = (B) i + (A) j
Compare both sides
100cos 60° = B
100 sin 60° = A
Solve for A and B
A = 100 sin 60°
B = 100 cos 60°
Substitute the values of sin 60° = 0.8660 and cos 60° = 0.5000
A = 100 x 0.86600 = 86.60N
B = 100 x 0.5000 = 50.00N
Therefore, the magnitude of the vector (B) that makes an angle of 60 with the resultant is 50.00N
Answer:
50 N and 86.6 N
Explanation:
Given that
R = 100 N
Cos 60° = 0.5
Sin 60° = 0.8660
Assume the first force is F1, so
F1 = 100 x cos 60
F1 = 100 x 0.5
F1 = 50 N
Assume that the second force is F2, so
F2 = 100 x sin 60
F2 = 100 x 0.866
F2 = 86.6 N approximately 87N
The magnitudes are 87 N and 50 N.
Check,
R = √(F1)² + (F2)²
R = √(50)² + (86.6)²
R = √2500 + 7500
R = √10000
R = 100 N
Therefore, since we checked from the gotten magnitude for our resultant, the answer is correct
