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.
Answer:
Incomplete question: "Each block has a mass of 0.2 kg"
The velocity of the center of mass for the two-block system just prior to their collision is 2.9489 m/s
Explanation:
Provided information:
θ = angle of the surface = 37°
m = mass of each block = 0.2 kg
v = speed = 0.35 m/s
t = collision time = 0.5 s
Question: What is the velocity of the center of mass for the two-block system right before the blocks collide, vf =?
Change in momentum:
It’s essential to calculate the required force:
Here, g = acceleration due to gravity = 9.8 m/s²
Answer:
The energy delivered is E = 0.18 J
Explanation:
Given,
Battery voltage, V = 9 V
Charge in the circuit, Q = 20 mC
= 20 x 10³ C
Energy supplied in the circuit can be computed as
E = Q V
E = 20 x 10⁻³ x 9
E = 180 x 10⁻³
E equals 0.18 J.
The energy delivered in the circuit is therefore E = 0.18 J
