As you brake your bicycle, your velocity changes from 20 east m/s to 10 east m/s in 5 seconds.

If vector A =i+2j-k and vec A cross vec B =3i-j+5k. find vec B

postnew [5]

Let B = a i + b j + c k. Then the cross product of A = i + 2j - k with B is

A × B = ( i + 2j - k ) × ( a i + b j + c k )

A × B = a ( i × i ) + 2a ( j × i ) - a ( k × i )

… … … + b ( i × j ) + 2b ( j × j ) - b ( k × j )

… … … + c ( i × k ) + 2c ( j × k ) - c ( k × k )

A × B = 0 - 2a k - a j

… … … + b k + 0 + b i

… … … - c j + 2c i - 0

A × B = (b + 2c) i + (-a - c) j + (b - 2a) k

So we have

3 i - j + 5 k = (b + 2c) i + (c - a) j + (b - 2a) k

which gives us the system of equations,

{ b + 2c = 3

{ -a - c = -1

{ -2a + b = 5

Solve for a, b, and c.

• Eliminate c from the first two equations:

(b + 2c) + 2 (-a - c) = 3 + 2 (-1)

-2a + b = 1

But -2a + b = 5, and 5 ≠ 1, so there is no such vector B that satisfies the cross product!

8 0

2 years ago

What state of matter can easily be compressed (squeezed into a much smaller space)? *

avanturin [10]

Answer:

gases.

Explanation:

gases have the highest volume. if you compress (increase pressure) a gas, the volume decreases and it will take up less space as a liquid, and if you compress more, the liquid will become a solid.

additionally info: this is generally true, but as you get into more difficult subjects, this rule does not hold. for example, some substances cannot obtain a certain phase of matter when they are a certain temperature and or pressure. but that could be way more out of this questions league.

6 0

2 years ago

What two gases probably dominated precambrian earth's atmosphere?

galben [10]

I think these gases are water vapor and nitrogen. As the temperature rises, these water vapor molecules, would condense and form the oceans we have. Also, it was said that in the early atmosphere, nitrogen is very abundant and even today the composition of air is 79% by volume.

8 0

3 years ago

An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 2530 km. When the astronaut jumps upwa

Natali [406]

Answer:

1.38*10^18 kg

Explanation:

According to the Newton's law of universal gravitation:

$F=G*\frac{m_a*m_p}{r^2}$

where:

G= Gravitational constant (6.674×10−11 N · (m/kg)2)

ma= mass of the astronaut

mp= mass of the planet

$F=m_a.a\\(v_f )^2=(v_o)^2+2.a.\Delta y\\\\a=\frac{(v_f)^2-(v_o)^2}{2.\Delta y}\\\\a=\frac{(0)^2-(4.29m/s)^2}{2.0.64m}=14.38m/s^2\\\\F=m_a*14.38m/s^2$

so:

$m_a*14.38m/s^2=(6.674*10^{-11}N.(m/kg)^2)*\frac{m_a.m_p}{(2.530*10^3m)^2}\\m_p=\frac{14.38m/s^2(2.530*10^3m)^2}{(6.674*10^{-11}N.(m/kg)^2)}\\\\m_p=1.38*10^{18}kg$

7 0

3 years ago

Doctor prescribed drug which is 500mg for patient change this unit into gram

ololo11 [35]

Answer:

.5 grams

Explanation:

1 gram is equal to 1000 milligrams (mg)

6 0

3 years ago