Q should be positioned 4.8 miles east of point B. Explanation: From the diagram, we can define the construction cost as a function of angle θ (as illustrated). The underwater pipe length (marked in blue) equals 6/cos θ, while the land pipe length (marked in brown) is (8 - 6*tan θ). The total construction cost formula is: Construction Cost = (6/cos θ)(6000) + (8 - 6*tan θ)(3750). This formula is represented in terms of θ, which can vary from 0 degrees to 53.13 degrees according to the diagram. To find the angle θ that minimizes the construction cost, we differentiate the Construction Cost function with respect to θ and set it to zero. The derivative yields: -4500(5*sec θ – 8*tan θ)(sec θ) = 0, leading to θ = 38.68 degrees. By substituting θ, we can determine the distance of Q from B, which equals 6*tan θ. This calculates to a distance of 4.8 miles.
The full question reads;
Jason is employed at a moving company. A wooden crate weighing 75 kg is positioned on the wooden ramp of his truck, inclined at an angle of 11°.
What is the force magnitude, directed parallel to the ramp, that he needs to apply to initiate the upward movement of the crate?
Answer:
F = 501.5 N
Explanation:
We have the following information;
Mass of the wooden crate; m = 75 kg
Incline angle; θ = 11°
To move the wooden crate up, we must consider that friction is acting in the opposite direction of the movement along the inclined surface. Therefore, the force required can be expressed by;
F = mgsin θ + μmg cos θ
Using online resources, the coefficient of friction between wooden surfaces is μ = 0.5
Thus;
F = (75 × 9.81 × sin 11) + (0.5 × 75 × 9.81 × cos 11)
F = 501.5 N
