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2 years ago

If a vector a - b = 2c, a + b = 4c and c = 3i + 4j,find a and b

1 answer:

6 0

Ans:
a = 9i + 12j
b = 3i + 4j

Explanation:
We have two equations:

a - b = 2c --- (A)
a + b = 4c --- (B)

and two unknowns:
a = ?
b = ?

Whereas,
c = 3i + 4j

Add equations (A) and (B):
=> a - b = 2c
a + b = 4c
----------------------
2a = 6c

=> a = 3c --- (C)
Put the value of vector c in equation (C):

(C) => a = 3(3i + 4j)
=> a = 9i + 12j

Now that we have vector a, put that vector and vector c in equation (A):
(A)=> (9i + 12j) - b = 2(3i + 4j)

=> b = (9i + 12) - (6i + 8j)
=> b = 3i + 4j

Ans:
a = 9i + 12j
b = 3i + 4j

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On a frictionless horizontal air table, puck A (with mass 0.254 kg ) is moving toward puck B (with mass 0.367 kg ), which is ini

irinina [24]

Answer:

$v_a=0.8176 m/s$

$\Delta K=0.07969 J - 0.0849 J = -0.00521 J$

Explanation:

According to the law of conservation of linear momentum, the total momentum of both pucks won't be changed regardless of their interaction if no external forces are acting on the system.

Being $m_a$ and $m_b$ the masses of pucks a and b respectively, the initial momentum of the system is

$M_1=m_av_a+m_bv_b$

Since b is initially at rest

$M_1=m_av_a$

After the collision and being $v'_a$ and $v'_b$ the respective velocities, the total momentum is

$M_2=m_av'_a+m_bv'_b$

Both momentums are equal, thus

$m_av_a=m_av'_a+m_bv'_b$

Solving for $v_a$

$v_a=\frac{m_av'_a+m_bv'_b}{m_a}$

$v_a=\frac{0.254Kg\times (-0.123 m/s)+0.367Kg (0.651m/s)}{0.254Kg}$

$v_a=0.8176 m/s$

The initial kinetic energy can be found as (provided puck b is at rest)

$K_1=\frac{1}{2}m_av_a^2$

$K_1=\frac{1}{2}(0.254Kg) (0.8176m/s)^2=0.0849 J$

The final kinetic energy is

$K_2=\frac{1}{2}m_av_a'^2+\frac{1}{2}m_bv_b'^2$

$K_2=\frac{1}{2}0.254Kg (-0.123m/s)^2+\frac{1}{2}0.367Kg (0.651m/s)^2=0.07969 J$

The change of kinetic energy is

$\Delta K=0.07969 J - 0.0849 J = -0.00521 J$

3 0

3 years ago

Which phrase best describes sir isaac newton's contributions to modern science and therefore to the industrial revolution?

astraxan [27]

Can you please give the phrases?

But, I'll help what I can.

First, he was the first to discover gravity. He was not bonked by the head by an apple, rather he watched an apple fall from a tree before he decided to explore gravity further.

He was also the first scientist to be knighted, which is a great honor, as you can expect.

Newton also developed The Three Laws of Motion. They are extremely important to physics and are considered some of the foundation for physics today.

He also discovered calculus, which is complex math that is very helpful to scientists today.

He also discovered the color spectrum using a glass prism, a dark room and window shade with a hole in it. He was able to project the color spectrum onto a piece of paper.

Those are the few I can think of now, but hope it helps!

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3 years ago

The higher the amplitude of the wave, the greater its intensity and the greater its loudness.

lyudmila [28]

True,when you turn the volume up on your television , you're actually turning up the amplitude!

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3 years ago

Consider the following possibilities and select the correct choice.

dezoksy [38]

Answer:

Tx not but mybe

Explanation:

for that reason its just trying to help

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2 years ago

What perspective of dream interpretation is being offered?

vitfil [10]

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