Recall the formula,
∆<em>θ</em> = <em>ω</em>₀ <em>t</em> + 1/2 <em>α</em> <em>t</em> ²
where ∆<em>θ</em> = angular displacement, <em>ω</em>₀ = initial angular speed (which is zero because the disk starts at rest), <em>α</em> = angular acceleration, and <em>t</em> = time. Solve for the acceleration with the given information:
50 rad = 1/2 <em>α</em> (5 s)²
<em>α</em> = (100 rad) / (25 s²)
<em>α</em> = 4 rad/s²
Now find the angular speed <em>ω </em>after 3 s using the formula,
<em>ω</em> = <em>ω</em>₀ + <em>α</em> <em>t</em>
<em>ω</em> = (4 rad/s²) (3 s)
<em>ω</em> = 12 rad/s
Answer:
Thrust developed = 212.3373 kN
Explanation:
Assuming the ship is stationary
<u>Determine the Thrust developed</u>
power supplied to the propeller ( Punit ) = 1900 KW
Duct distance ( diameter ; D ) = 2.6 m
first step : <em>calculate the area of the duct </em>
A = π/4 * D^2
= π/4 * ( 2.6)^2 = 5.3092 m^2
<em>next : calculate the velocity of propeller</em>
Punit = (A*v*β ) / 2 * V^2 ( assuming β = 999 kg/m^3 ) also given V1 = 0
∴V^3 = Punit * 2 / A*β
= ( 1900 * 10^3 * 2 ) / ( 5.3092 * 999 )
hence V2 = 8.9480 m/s
<em>Finally determine the thrust developed </em>
F = Punit / V2
= (1900 * 10^3) / ( 8.9480)
= 212.3373 kN
Answer:
Changes in the object's momentum (answer D)
Explanation:
A net force will cause an object to change its velocity, and that will affect the object's momentum, which is defined by the product of the object's mass times its velocity.
So, select the last option (D) in the given list.
Answer;
B. Increased levels of carbon dioxide, a greenhouse gas, leads to increased phytoplankton growth.
Explanation;
-A combination of warm water, high nutrient levels, and adequate sunlight may cause a harmful algae bloom. These blooms may damage aquatic ecosystems by blocking sunlight and depleting oxygen that other organisms need to survive.
-Algae blooms have been increasing globally, and climate change may be playing a role in the increment. For instance, during the warm summer season or when water is warmer, some harmful types of algae to grow faster than other, more benign varieties.
-Additionally, the warmer surface water also prevents water from mixing vertically, allowing algae to grow thicker and faster.
Answer:
v₀ = 3.77 [m/s]
Explanation:
This problem can be solved in a simple way by means of the following equation of kinematics.
where:
y - yo = 0.441 [m]
Vo = initial velocity [m/s]
g = gravity acceleration = 9.81 [m/s²]
t = time = 0.625 [s]
![0.441 = v_{o}*(0.625)-\frac{1}{2} *9.81*(0.625)^{2} \\2.357 = v_{o}*0.625\\v_{o}=3.77[m/s]](https://tex.z-dn.net/?f=0.441%20%3D%20v_%7Bo%7D%2A%280.625%29-%5Cfrac%7B1%7D%7B2%7D%20%2A9.81%2A%280.625%29%5E%7B2%7D%20%5C%5C2.357%20%3D%20v_%7Bo%7D%2A0.625%5C%5Cv_%7Bo%7D%3D3.77%5Bm%2Fs%5D)
Note: The sign of the acceleration is negative since the movement of the basketball player is against of the gravity acceleration.
