A 60 kg hockey player skating at 20 m/s gets slammed with a force of 950 N. How long does it take him to stop completely?

Assume that the amplifiers on the stage operate at a combined power of 5,000 Watts, and that 80% of this is converted to sound.

rusak2 [61]

Answer:

0.04

Explanation:

Fraction of power converted to sound = 80% = 0.08

Fraction incident upon each eardrum onstage = 0.08/2 = 0.04

6 0

3 years ago

Two boats leave the same port at the same time, with boat A traveling north at 15 knots (nautical miles per hour) and boat B tra

Mrrafil [7]

Answer:

The chance in distance is 25 knots

Explanation:

The distance between the two particles is given by:

$s^2 = (x_A - x_B)^2+(y_A - y_B)^2$ (1)

Since A is traveling north and B is traveling east we can say that their displacement vector are perpendicular and therefore (1) transformed as:

$s^2 = x_B^2+y_A^2$ (2)

Taking the differential with respect to time:

$\displaystyle{2s\frac{ds}{dt}= 2x_B\frac{dx_B}{dt}+2y_A\frac{dy_A}{dt}}$ (3)

where $\displaystyle{\frac{dx_B}{dt}}=v_B$ and $\displaystyle{\frac{dx_A}{dt}}=v_A$ are the respective given velocities of the boats. To find $s$ and $x_B$ we make use of the given position for A, $y_A=30$ , the Pythagoras theorem and the relation between distance and velocity for a movement with constant velocity.

$\displaystyle{y_A = v_A\cdot t\rightarrow t = \frac{y_A}{v_A}=\frac{30}{15}=2 h$

with this time, we know can now calculate the distance at which B is:

$\displaystyle{x_B = v_B\cdot t= 20 \cdot 2 = 40\ nmi$

and applying Pythagoras:

$\displaystyle{s = \sqrt{x_B^2+y_A^2}=\sqrt{30^2 + 40^2}=\sqrt{2500}=50}$

Now substituting all the values in (3) and solving for $\displaystyle{\frac{ds}{dt} }$ we get:

$\displaystyle{\frac{ds}{dt} = \frac{1}{2s}(2x_B\frac{dx_B}{dt}+2y_A\frac{dy_A}{dt})}\\\displaystyle{\frac{ds}{dt} = 25 \ knots}$

4 0

2 years ago

Write the equation expressing the relationship "y varies directly as x." use k as the constant of proportionality.

Alexeev081 [22]

The equation expressing the statement "y varies directly as x" is $y=kx.$

Explanation

The statement that $y$ varies directly as $x$ is analogous to saying that the ratio of $y$ to $x$ is constant. In other words, when $x$ increases, $y$ likewise increases and that when $x$ decreases, $y$ decreases proportionally.

Mathematically, we express the relationship that the ration of $y$ is to $x$ is constant is expressed as; $\frac{y}{x} =k$ where $k$ is the constant of proportionality.

We can then solve the relationship for $y$ to determine the correct form of the relationship as shown below,

$\frac{y}{x} =k\\\rightarrow y=kx$

6 0

2 years ago

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When bones are moved by muscles due to

77julia77 [94]

Respiratory and circulatory

6 0

2 years ago

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In the graph, which region shows nonuniform positive acceleration?

cricket20 [7]

Answer: A.AB

Explanation:

This Velocity vs Time graph shows the acceleration of a body or object, since acceleration is the variation of velocity in time.

As we can see in the attached image, the graph can be divided in four segments:

OA: In this segment the acceleration is changing at a uniform rate. In addition we can see it has a positive slope, hence we are dealing with a positive uniform acceleration.

AB: In this segment the acceleration is changing at a nonuniform rate, since in this part it is not possible to calculate the slope. However if this were uniform, the slope woul be positive. This means the <u>acceleration is nonuniform and positive.</u>

BC: In this segment the acceleration is changing at a nonuniform rate, since in this part it is not possible to calculate the slope. However if this were uniform, the slope woul be negative. This means the acceleration is nonuniform and negative.

CD: In this segment the acceleration is changing at a uniform rate. In addition we can see it has a negative slope, hence we are dealing with a negative uniform acceleration.

From all these segments, the only one that fulfils the nonuniform positive acceleration condition is option A:

Segment AB

3 0

2 years ago

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