The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
Answer:
D: Increase the distance between the objects.
E: Decrease the mass of one of the objects.
- Mass of the elevator (m) = 570 Kg
- Acceleration = 1.5 m/s^2
- Distance (s) = 13 m
- Let the force be F.
- We know, F = ma,
- Therefore, F = (570 × 1.5) N = 855 N
- Angle between distance and force (θ) = 0°
- We know, work done = F s Cos θ
- Therefore, work done by the cable during this part
- = (855 × 13 × Cos 0°) J
- = (855 × 13 × 1) J
- = 11115 J
<u>Answer</u><u>:</u>
<u>1</u><u>1</u><u>1</u><u>1</u><u>5</u><u> </u><u>J</u>
Hope you could get an idea from here.
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