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marta [7]
2 years ago
15

The Cartesian coordinate of a point in the xy plane are (x,y)=(-3.50,-2.50)m. Find the poler coordinate of this point

Physics
1 answer:
Masja [62]2 years ago
5 0

Answer:

The polar coordinate of P(x,y) = (-3.50\,m,-2.50\,m) is P (r,\theta) = (4.301\,m, 215.538^{\circ}).

Explanation:

Given a point in rectangular form, that is P(x,y) = (x,y), its polar form is defined by:

P(x,y) = (r,\theta) (1)

Where:

r - Norm, measured in meters.

\theta - Direction, measured in sexagesimal degrees.

The norm of the point is determined by Pythagorean Theorem:

r = \sqrt{x^{2}+y^{2}} (2)

And direction is calculated by following trigonometric relation:

\theta = \tan^{-1} \frac{y}{x} (3)

If we know that x = -3.50\,m and y = -2.50\,m, then the components of coordinates in polar form is:

r = \sqrt{(-3.50\,m)^{2}+(-2.50\,m)^{2}}

r \approx 4.301\,m

Since x < 0\,m and y < 0\,m, direction is located at 3rd Quadrant. Given that tangent function has a period of 180º, we find direction by using this formula:

\theta = 180^{\circ}+\tan^{-1} \left(\frac{-2.50\,m}{-3.50\,m} \right)

\theta \approx 215.538^{\circ}

The polar coordinate of P(x,y) = (-3.50\,m,-2.50\,m) is P (r,\theta) = (4.301\,m, 215.538^{\circ}).

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Answer:

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The angle at which the particle 9m is scattered is \theta = -66,68^{o} with respect to the - y axis.

Explanation:

In an elastic collision the total linear momentum and the total kinetic energy is conserved.

<u>Conservation of linear momentum:</u>

Because the linear momentum is a vector quantity we consider the conservation of the components of momentum in the x and y axis.

The subindex 1 will refer to the particle 9m and the subindex 2 will refer to the particle 2m

\vec{p}=m\vec{v}

p_{xi} =p_{xf}

In the x axis before the collision we have

p_{xi}=9m\ v_{i} - 2m\ v_{i}

and after the collision we have that

p_{xf} =9m\ v_{1x}

In the y axis before the collision p_{yi} =0

after the collision we have that

p_{yf} =9m\ v_{1y} - 2m\ v_{2y}

so

p_{xi} =p_{xf} \\7m\ v_{i} =9m\ v_{1x}\Rightarrow v_{1x} =\frac{7}{9}\ v_{i}

then

p_{yi} =p_{yf} \\0=9m\ v_{1y} -2m\ v_{2y} \\v_{1y}=\frac{2}{9} \ v_{2y}

<u>Conservation of kinetic energy:</u>

\frac{1}{2}\ 9m\ v_{i} ^{2} +\frac{1}{2}\ 2m\ v_{i} ^{2}=\frac{1}{2}\ 9m\ v_{1f} ^{2} +\frac{1}{2}\ 2m\ v_{2f} ^{2}

so

\frac{11}{2}\ m\ v_{i} ^{2} =\frac{1}{2} \ 9m\ [(\frac{7}{9}) ^{2}\ v_{i} ^{2}+ (\frac{2}{9}) ^{2}\ v_{2y} ^{2}]+ m\ v_{2y} ^{2}

Putting in one side of the equation each speed we get

\frac{25}{9}\ m\ v_{i} ^{2} =\frac{11}{9}\ m\ v_{2y} ^{2}\\v_{2y} =-1,51\ v_{i}

We know that the particle 2m travels in the -y axis because it was stated in the question.

Now we can get the y component of the  speed of the 9m particle:

v_{1y} =\frac{2}{9}\ v_{2y} \\v_{1y} =-0,335\ v_{i}

the magnitude of the final speed of the particle 9m is

v_{1f} =\sqrt{v_{1x} ^{2}+v_{1y} ^{2} }

v_{1f} =\sqrt{(\frac{7}{9}) ^{2}\ v_{i} ^{2}+(-0,335)^{2}\ v_{i} ^{2} }\Rightarrow \ v_{1f} =0,85\ v_{i}

The tangent that the speed of the particle 9m makes with the -y axis is

tan(\theta)=\frac{v_{1x} }{v_{1y}} =-2,321 \Rightarrow\theta=-66,68^{o}

As a vector the speed of the particle 9m is:

\vec{v_{1f} }=\frac{7}{9} v_{i} \hat{x}-0,335\ v_{i}\ \hat{y}

As a vector the speed of the particle 2m is:

\vec{v_{2f} }=-1,51\ v_{i}\ \hat{y}

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As the given reaction is an exothermic reaction in which the heat is released during a chemical reaction. That means the temperature is decreased on the reactant side.

For an exothermic reaction, heat is released during a chemical reaction and is written on the product side.

A\rightleftharpoons B+\text{ heat}

If the temperature is increases in the equilibrium then the equilibrium will shift in the direction where, temperature is getting decreased. Thus, the reaction will shift to the left direction i.e, towards the reactant.

Hence, when we increase the temperature of an exothermic reaction the equilibrium will shift to the left direction i.e, towards the reactant.

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Answer:

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here we know that

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f = \frac{v}{4L}

1398.6 = \frac{340}{4L}

L = 0.06 m

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What occurs when someone places an ice pack on an injured ankle?
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The answer is:

Heat from the ankle is transferred to the ice pack.

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Heat will transfer from the ankle to the ice pack.

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