Physics, 28.07.2021 23:40 paigeisawesome

given A=4i-10j and B= 7i+5j find b such that A+bB is a vector pointing along the x-axis (i. e has no y component)

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Answer from: thelonewolf5020

-4/7

Explanation:

Given the following

A=4i-10j and B= 7i+5j

A+ bB = 4i-10j + (7i+5j)b

A+ bB = 4i-10j + 7ib+5jb

A+ bB =

The vector along the x-axis is expressed as i + 0j

If the vector A+ bB is pointing in the direction of the x-axis then;

$A+ bB * \frac{i+0j}{|i+0j|} = 0 \\ (4+7b)i-(10-5b)j* \frac{i+0j}{\sqrt{1^2+0^2} } = 0\\(4+7b)i-(10-5b)j *(i+0j) = 0\\4+7b-0 =0\\7b=-4\\b = -4/7$

Hence the value of b is -4/7

Answer from: andrecoral105

The value of $\beta$ such that $\vec C = \vec A + \beta \cdot \vec B = c\,\hat{i}$ is 2.

According to the statement, we have following system of vectorial equations:

$\vec A = 4\,\hat {i} - 10\,\hat{j}$ (1)

$\vec {B} = 7\,\hat{i} + 5\,\hat{j}$ (2)

$\vec C = \vec A + \beta \cdot \vec B = c\,\hat{i}$ (3)

By applying (1) and (2) in (3):

$(4\,\hat{i}-10\,\hat{j}) + \beta\cdot (7\,\hat{i}+5\,\hat{j}) = c\,\hat{i}$

$(4+7\cdot \beta)\,\hat{i} +(-10+5\cdot \beta)\,\hat{j} = c\,\hat{i}$

And we get two scalar equations after analyzing each component:

$4+7\cdot \beta = c$ (4)

$-10+5\cdot \beta = 0$ (5)

We solve for $\beta$ in (5):

$\beta = 2$

And for in (4):

$c = 4+7\cdot (2)$

c = 18

The value of $\beta$ such that $\vec C = \vec A + \beta \cdot \vec B = c\,\hat{i}$ is 2.

Please see this question related to Sum of Vectors for further details:

Answer from: Quest

The figure is missing but we can answer anyway.the correct answer is "releasing the string". in fact, when the person is holding the bow and the arrow, the kinetic energy of the arrow is still zero (because the arrow is not moving). the moment the arrow is released, it acquires a velocity v, so its kinetic energy will become different from zero: $k= \frac{1}{2}mv^2$ where m is the mass of the arrow and v its velocity. all the other options, instead, do not increase the kinetic energy of the system: - pulling farther back on the string : this will just increase the elastic potential energy of the system- holding the arrow higher: this will increase the gravitational potential energy of the system (which is given by u=mgh, where h is the height above the ground)- decreasing the mass of the arrow: this will decrease the gravitational potential energy of the system (which is given by u=mgh, where m is the mass)

Answer from: Quest

if i am correct, your answer choices are:

a. the temperature remains constant

b. the temperature increases at a constant rate

c. heat flows at a constant rate into the system

d. heat flows at a constant rate out of the system

e. no heat flows into or out of the system

if so, then the answer is e. no heat flows into or out of the system.