The correct answer among the choices is option D. Density is not one of the properties included in the ideal gas law. The law is expressed as: PV=nRT. As we can see, the pressure, the volume and the temperature of the gas are included in the law.
Relative to the positive horizontal axis, rope 1 makes an angle of 90 + 20 = 110 degrees, while rope 2 makes an angle of 90 - 30 = 60 degrees.
By Newton's second law,
- the net horizontal force acting on the beam is

where
are the magnitudes of the tensions in ropes 1 and 2, respectively;
- the net vertical force acting on the beam is

where
and
.
Eliminating
, we have





Solve for
.



<h2>
Resultant is 235.54 pounds at an angle 44.16° to X axis.</h2>
Explanation:
Forces are 100 pound and 150 pound and angles with x axis are 20°and 60°.
That is force 1 is 100 pound with x axis at 20°
F₁ = 100 cos 20 i + 100 sin 20 j
F₁ = 93.97 i + 34.20 j
That is force 2 is 150 pound with x axis at 60°
F₂ = 150 cos 60 i + 150 sin 60 j
F₂ = 75 i + 129.90 j
F₁ + F₂ = 93.97 i + 34.20 j + 75 i + 129.90 j
F₁ + F₂ = 168.97 i + 164.10 j

Resultant is 235.54 pounds at an angle 44.16° to X axis.
This question involves the concepts of dynamic pressure, volume flow rate, and flow speed.
It will take "5.1 hours" to fill the pool.
First, we will use the formula for the dynamic pressure to find out the flow speed of water:

where,
v = flow speed = ?
P = Dynamic Pressure = 55 psi
= 379212 Pa
= density of water = 1000 kg/m³
Therefore,

v = 27.54 m/s
Now, we will use the formula for volume flow rate of water coming from the hose to find out the time taken by the pool to be filled:

where,
t = time to fill the pool = ?
A = Area of the mouth of hose =
= 1.98 x 10⁻⁴ m²
V = Volume of the pool = (Area of pool)(depth of pool) = A(1.524 m)
V =
= 100.1 m³
Therefore,

<u>t = 18353.5 s = 305.9 min = 5.1 hours</u>
Learn more about dynamic pressure here:
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