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4 years ago

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Suppose I have a vector that is 7 units long and that makes an angle of +30 degrees from the positive x-axis. I want to add to t

his a vector that is also 7 units long and that makes an angle of 120 degrees from the positive x-axis. What is the correct (x,y) representation of the sum of these two vectors?

1 answer:

Vinil7 [7]4 years ago

5 0

Answer:

sum of these two vectors is 6.06i+3.5j-3.5i+6.06j = 2.56i+9.56j

Explanation:

We have given first vector which has length of 7 units and makes an angle of 30° with positive x-axis

So x component of the vector $=7cos30^{\circ}=7\times 0.866=6.06$

y component of the vector $=7sin30^{\circ}=7\times 0.5=3.5$

So vector will be 6.06i+3.5j

Now other vector of length of 7 units and makes an angle of 120° with positive x-axis

So x component of vector $=7cos120^{\circ}=7\times -0.5=-3.5i$

y component of the vector $=7sin120^{\circ}=7\times 0.866=6.06j$

Now sum of these two vectors is 6.06i+3.5j-3.5i+6.06j = 2.56i+9.56j

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The answer is $v=15.6 \mathrm{~km} / \mathrm{s}$ .

<h3>What is kinetic energy?</h3>

A particle or an item that is in motion has a sort of energy called kinetic energy. An item accumulates kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force.
Kinetic energy comes in five forms: radiant, thermal, acoustic, electrical, and mechanical.
The energy of a body in motion, or kinetic energy (KE), is essentially the energy of all moving objects. Along with potential energy, which is the stored energy present in objects at rest, it is one of the two primary types of energy.
Explain that a moving object's mass and speed are two factors that impact the amount of kinetic energy it will possess.

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$U_1=-\frac{G M_{\mathrm{G}} m}{R_G}$

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when it is on the surface of the Ganymede is,

$U_2=-\frac{G M_{\mathrm{J}} m}{R}$

Here, R is a separation between Jupiter and Ganymede.

To escape from the surface of Ganymede potential energy of the rocket due to Jupiter and Ganymede is equal to the kinetic energy of the rocket.

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$v^2=\frac{2 G M_{\mathrm{G}}}{R_G}+\frac{2 G M_{\mathrm{T}}}{R}$

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$v=15.6 \mathrm{~km} / \mathrm{s}$

To learn more about kinetic energy, refer to:

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As you can see the results are identical.

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3 years ago