Answer:
v2 = 65 m/s
the speed of the water leaving the nozzle is 65 m/s
Explanation:
Given;
Water flows at 0.65 m/s through a 3.0 cm diameter hose that terminates in a 0.3 cm diameter nozzle
Initial speed v1 = 0.65 m/s
diameter d1 = 3.0 cm
diameter (nozzle) d2 = 0.3 cm
The volumetric flow rates in both the hose and the nozzle are the same.
V1 = V2 ........1
Volumetric flow rate V = cross sectional area × speed of flow
V = Av
Area = (πd^2)/4
V = v(πd^2)/4 ....2
Substituting equation 2 to 1;
v1(πd1^2)/4 = v2(πd2^2)/4
v1d1^2 = v2d2^2
v2 = (v1d1^2)/d2^2
Substituting the given values;
v2 = (0.65 × 3^2)/0.3^2
v2 = 65 m/s
the speed of the water leaving the nozzle is 65 m/s
Option (ii) B is the correct option. The object on the moon has greater mass.
To resolve this, utilize the formulas Force = Mass * Acceleration.
The equation can be used to find the mass given the force in Newtons, using 9.8 m/s² for the acceleration of gravity of the earth and 1.6 m/s² for the moon.
Calculating the mass on earth:
30 N = 9.8 m/s² * mass
This results in a mass of 3.0 kg for the object on Earth.
Calculating the mass of the moon:
30 N = 1.6 m/s²2 * mass
Thus, the moon's object has a mass of 19. kg.
This can be explained by the fact that the earth has a stronger gravitational pull than the moon, producing more force per kilogram of mass. As a result, the moon's mass must be bigger to produce the same amount of force at a lower acceleration from gravity (1.6 m/s² vs. 9.8 m/s²).
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The velocity of the ball is 12.5 m/s
Explanation:
The velocity of the ball is given by the ratio between the distance covered by the ball and the time taken:

First, we calculate the distance covered. We know that the radius of the circle is
r = 0.450 m
And the length of the circumference is

The ball makes 25.0 revolutions, so a total distance of

In a time of
t = 9.37 s
So, its velocity is

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Answer and Explanation:
1. Evaluate the function x(t) at t=0.5

2. The period of motion T can be calculated as:

Where:

So:

3. The angular frequency can be expressed as:

Solving for k:

4. Find the derivate of x(t):

Now, the sine function reach its maximum value at π/2 so:

Solving for t:

Evaluating v(t) for 0.6603981634:

So the maximum speed of the block is:
In the negative direction of x-axis
5. The force is given by:

The cosine function reach its maximum value at 2π so:

Solving for t:

Evaluating x(t) for 3.016592654:

Therefore the the maximum force on the block is:
