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>
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<h2>The man have to apply force of 160 N</h2>
Explanation:
The work done to lift the bag of weight mg through height 2.5 m is 400 J
The work done can be found by relation W = mg x h
Thus mg =
=
= 160 N
Therefore the man have to apply the force of 160 N
Answer:
The semi truck travels at an initial speed of 69.545 meters per second downwards.
Explanation:
In this exercise we see a case of an entirely inellastic collision between the semi truck and the car, which can be described by the following equation derived from Principle of Linear Momentum Conservation: (We assume that velocity oriented northwards is positive)
(1)
Where:
,
- Masses of the semi truck and the car, measured in kilograms.
,
- Initial velocities of the semi truck and the car, measured in meters per second.
- Final speed of the system after collision, measured in meters per second.
If we know that
,
,
and
, then the initial velocity of the semi truck is:





The semi truck travels at an initial speed of 69.545 meters per second downwards.
Explanation:
The attached figure shows data for the cart speed, distance and time.
For low fan speed,
Distance, d = 500 cm
Time, t = 7.4 s
Average velocity,

Acceleration,

For medium fan speed,
Distance, d = 500 cm
Time, t = 6.4 s
Average velocity,

Acceleration,

For high fan speed,
Distance, d = 500 cm
Time, t = 5.6 s
Average velocity,

Acceleration,

Hence, this is the required solution.
Explanation:
Mass of the astronaut, m₁ = 170 kg
Speed of astronaut, v₁ = 2.25 m/s
mass of space capsule, m₂ = 2600 kg
Let v₂ is the speed of the space capsule. It can be calculated using the conservation of momentum as :
initial momentum = final momentum
Since, initial momentum is zero. So,



So, the change in speed of the space capsule is 0.17 m/s. Hence, this is the required solution.