Answer:
a) v = 1.19 m/s, b) P₁ = 0.922 x 10⁵ Pa
Explanation:
1) We will apply the fluid continuity equation
Q = A v
The area of a circle is
A = π r² = π d²/4
v = Q / A = Q 4 / π d²
v = 0.006 4/π 0.08²
v = 1.19 m/s
2) Apply Bernoulli's equation, considering point 1 as the bladder and point 2 as where the urine exits
P₁ + ½ ρ v₁² + ρ g y₁ = P₂ + ½ ρ v₂² + ρ g y₂
The problem states that
P₂ = 1.0013 x 10⁵ Pa
v₁ = 0
y₁ = 1 m
y₂ = 0
Density of water (ρ) = 1000 kg/m³
P₁ + ρ y₁ = P₂ + ½ ρ v₂²
P₁ = P₂ + ½ ρ v₂² - ρ g y₁
P₁ = 1.013 x 10⁵ + ½ 1000 (1.19)² - 1000 9.8 1
P₁ = 1.013 x 10⁵ + 708.5 - 9800
P₁ = 92208.5 Pa
P₁ = 0.922 x 10⁵ Pa
The responses would be:
C. Bubbles form
E. There is a change in color
For further details, feel free to explore:
While the chosen answers are indicative of chemical reactions, if you are solely referring to the chemical reaction in your example, these two answers represent the only options.
A chemical reaction occurs when reactants create a new substance. Indicators of a chemical reaction include alterations in smell, color, and temperature. At times, precipitates may develop.
The resultant velocity is 12.5 m/s North/east. I visualized it as a graph, determining the distance between the coordinates (0,0) and (10, 7.5).
Response:
The ball remained airborne for 3.896 seconds
Explanation:
Given that
g = 9.8 m/s², representing gravitational acceleration,
If the angle of launch is 45°, the horizontal range will be maximized.
Both horizontal and vertical launch velocities are equal, each equating to
v_h = v cos θ
v_h = 27 × cos 45°
= 19.09 m/s.
The duration to reach maximum height is half of the flight time.
v = u + at ∵ v = 0 (at maximum height)
19.09 - 9.8 t₁ = 0
t₁ = 1.948 s
The total time in the air equals twice the time to reach maximum height
2 t₁ = 3.896 s
The horizontal distance covered is
D = v × t
D = 3.896×19.09
= 74.375 m
The ball was in the air for 3.896 seconds
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