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FromTheMoon [43]
3 years ago
15

Question 2: Start-Up

Physics
1 answer:
yuradex [85]3 years ago
7 0

Answer:

The car starts moving in the positive direction at x = 0.2 seconds. Initially it moves very little, but it covers a greater distance with each time increment.

Explanation:

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Red light has a wavelength of 500 nm. What is the frequency of red light?
snow_tiger [21]

Answer:

0.6 \times 10 {}^{15}

Explanation:

By using relation,

Speed of light = frequency × wavelength (in m)

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3 years ago
How do scientists determine where an earthquake starts?
azamat
Scientists use a method called triangulation to determine where the earthquake was. It is called triangulation because a triangle has three sides, and it takes three seismographs to locate an earthquake.
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A net force of 500 N acts on a 100 kg cart. What is the acceleration of the cart if the mass is doubled?
oksian1 [2.3K]

Answer:

2.5 m/s²

Explanation:

You can solve the following equation: F=ma for acceleration.

You'll be left with this:

a=F/m

And then you substitute the force and the doubled mass

a=500N/200kg

a=2.5 m/s²

8 0
3 years ago
For this discussion, you will work in groups to answer the questions. In a video game, airplanes move from left to right along t
Mariulka [41]

Answer:

When fired from (1,3) the rocket will hit the target at (4,0)

When fired from (2, 2.5) the rocket will hit the target at (12,0)

When fired from (2.5, 2.4) the rocket will hit the target at (\frac{35}{2},0)

When fired from (4,2.25) the rocket will hit the target at (40,0)

Explanation:

All of the parts of the problem are solved in the same way, so let's start with the first point (1,3).

Let's assume that the rocket's trajectory will be a straight line, so what we need to do here is to find the equation of the line tangent to the trajectory of the airplane and then find the x-intercept of such a line.

In order to find the line tangent to the graph of the trajectory of the airplane, we need to start by finding the derivative of such a function:

y=2+\frac{1}{x}

y=2+x^{-1}

y'=-x^{-2}

y'=-\frac{1}{x^{2}}

so, we can substitute the x-value of the given point into the derivative, in this case x=1, so:

y'=-\frac{1}{x^{2}}

y'=-\frac{1}{(1)^{2}}

m=y'=-1

so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:

y-y_{1}=m(x-x_{1})

y-3=-1(x-1})

y-3=-1x+1

y=-x+1+3

y=-x+4

So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.

-x+4=0

and solve for x

x=4

so, when fired from (1,3) the rocket will hit the target at (4,0)

Now, let's calculate the coordinates where the rocket will hit the target if fired from (2, 2.5)

so, we can substitute the x-value of the given point into the derivative, in this case x=2, so:

y'=-\frac{1}{x^{2}}

y'=-\frac{1}{(2)^{2}}

m=y'=-\frac{1}{4}

so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:

y-y_{1}=m(x-x_{1})

y-2.5=-\frac{1}{4}(x-2})

y-2.5=-\frac{1}{4}x+\frac{1}{2}

y=-\frac{1}{4}x+\frac{1}{2}+\frac{5}{2}

y=-\frac{1}{4}x+3

So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.

-\frac{1}{4}x+3=0

and solve for x

x=12

so, when fired from (2, 2.5) the rocket will hit the target at (12,0)

Now, let's calculate the coordinates where the rocket will hit the target if fired from (2.5, 2.4)

so, we can substitute the x-value of the given point into the derivative, in this case x=2.5, so:

y'=-\frac{1}{x^{2}}

y'=-\frac{1}{(2.5)^{2}}

m=y'=-\frac{4}{25}

so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:

y-y_{1}=m(x-x_{1})

y-2.4=-\frac{4}{25}(x-2.5})

y-2.4=-\frac{4}{25}x+\frac{2}{5}

y=-\frac{4}{25}x+\frac{2}{5}+2.4

y=-\frac{4}{25}x+\frac{14}{5}

So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.

-\frac{4}{25}x+\frac{14}{5}=0

and solve for x

x=\frac{35}{20}

so, when fired from (2.5, 2.4) the rocket will hit the target at (\frac{35}{2},0)

Now, let's calculate the coordinates where the rocket will hit the target if fired from (4, 2.25)

so, we can substitute the x-value of the given point into the derivative, in this case x=4, so:

y'=-\frac{1}{x^{2}}

y'=-\frac{1}{(4)^{2}}

m=y'=-\frac{1}{16}

so we can now use this slope and the point-slope form of the line to find the equation of the line tangent to the trajectory of the airplane so we get:

y-y_{1}=m(x-x_{1})

y-2.25=-\frac{1}{16}(x-4})

y-2.25=-\frac{1}{16}x+\frac{1}{4}

y=-\frac{1}{16}x+\frac{1}{4}+2.25

y=-\frac{1}{16}x+\frac{5}{2}

So we can now set y=0 so find the x-coordinate where the rocket hits the x-axis.

-\frac{1}{16}x+\frac{5}{2}=0

and solve for x

x=40

so, when fired from (4,2.25) the rocket will hit the target at (40,0)

I uploaded a graph that represents each case.

8 0
3 years ago
g A ball thrown straight up into the air is found to be moving at 7.94 m/s after falling 2.72 m below its release point. Find th
kati45 [8]

The ball has height <em>y</em> and velocity <em>v</em> at time <em>t</em> according to

<em>y</em> = <em>v</em>₀ <em>t</em> - 1/2 <em>g</em> <em>t</em> ²

and

<em>v</em> = <em>v</em>₀ - <em>g t</em>

where <em>v</em>₀ is its initial speed and <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity.

The ball is falling with a velocity of 7.94 m/s when it's 2.72 m below the release point, which at time <em>t </em>such that

-2.72 m = <em>v</em>₀ <em>t</em> - 1/2 <em>g</em> <em>t</em> ²

-7.94 m/s = <em>v</em>₀ - <em>g t</em>

Solve for <em>t</em> in the second equation:

<em>t </em>= (<em>v</em>₀ + 7.94 m/s)/<em>g</em>

Substitute this into the first equation and solve for <em>v</em>₀ :

-2.72 m = <em>v</em>₀ (<em>v</em>₀ + 7.94 m/s) /<em>g</em> - 1/2 <em>g</em> ((<em>v</em>₀ + 7.94 m/s)/<em>g</em>)²

-2.72 m = <em>v</em>₀²/<em>g</em> + (7.94 m/s) <em>v</em>₀/<em>g</em> - 1/2 (<em>v</em>₀ + 7.94 m/s)²/<em>g</em>

2 (-2.72 m) <em>g</em> = 2<em>v</em>₀² + 2 (7.94 m/s) <em>v</em>₀ - (<em>v</em>₀ + 7.94 m/s)²

2 (-2.72 m) (9.80 m/s²) = 2<em>v</em>₀² + (15.9 m/s) <em>v</em>₀ - (<em>v</em>₀² + (15.9 m/s) <em>v</em>₀ + 63.0 m²/s²)

-53.3 m²/s² = <em>v</em>₀² - 63.0 m²/s²

<em>v</em>₀² = 9.73 m²/s²

<em>v</em>₀ = 3.12 m/s

3 0
3 years ago
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