Answer:
As the launch force increase the launch velocity will
<em><u>Increase</u></em>
The reason for your answer to number six is because
<em><u>There is a direct relationship between force and acceleration.</u></em>
<em><u /></em>
Explanation:
<em>It is known all over the place that, there is a direct relationship between Force and acceleration of an object leading to an increase in force being directly proportional to the increase in the acceleration of the given object and vice versa.</em>
Radiation because it radiates the heat in there body therefore making them hot.
Answer:
a) (0, -33, 12)
b) area of the triangle : 17.55 units of area
Explanation:
<h2>
a) </h2>
We know that the cross product of linearly independent vectors
and
gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.
Luckily for us, we know that vectors
and
are living in the plane through the points P, Q, and R, and are linearly independent.
We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).
If they weren't linearly independent, we will obtain vector zero as the result of the cross product.
So, for our problem:
![\vec{A} = \vec{P} - \vec{Q} \\\\\vec{A} = (1,0,1) - (-2,1,4)\\\\\vec{A} = (1 +2,0-1,1-4)\\\\\vec{A} = (3,-1,-3)](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%3D%20%5Cvec%7BP%7D%20-%20%5Cvec%7BQ%7D%20%5C%5C%5C%5C%5Cvec%7BA%7D%20%3D%20%281%2C0%2C1%29%20-%20%28-2%2C1%2C4%29%5C%5C%5C%5C%5Cvec%7BA%7D%20%3D%20%281%20%2B2%2C0-1%2C1-4%29%5C%5C%5C%5C%5Cvec%7BA%7D%20%3D%20%283%2C-1%2C-3%29)
![\vec{B} = \vec{R} - \vec{Q} \\\\\vec{B} = (6,2,7) - (-2,1,4)\\\\\vec{B} = (6 +2,2-1,7-4)\\\\\vec{B} = (8,1,3)](https://tex.z-dn.net/?f=%5Cvec%7BB%7D%20%3D%20%5Cvec%7BR%7D%20-%20%5Cvec%7BQ%7D%20%5C%5C%5C%5C%5Cvec%7BB%7D%20%3D%20%286%2C2%2C7%29%20-%20%28-2%2C1%2C4%29%5C%5C%5C%5C%5Cvec%7BB%7D%20%3D%20%286%20%2B2%2C2-1%2C7-4%29%5C%5C%5C%5C%5Cvec%7BB%7D%20%3D%20%288%2C1%2C3%29)
![\vec{A} \times \vec{B} = (A_y B_z - B_y A_z) \ \hat{i} - ( A_x B_z-B_xA_z) \ \hat{j} + (A_x B_y - B_x A_y ) \ \hat{k}](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%5Ctimes%20%20%5Cvec%7BB%7D%20%3D%20%28A_y%20B_z%20-%20B_y%20A_z%29%20%5C%20%20%5Chat%7Bi%7D%20-%20%28%20A_x%20B_z-B_xA_z%29%20%5C%20%5Chat%7Bj%7D%20%2B%20%28A_x%20B_y%20-%20B_x%20A_y%20%29%20%5C%20%5Chat%7Bk%7D)
![\vec{A} \times \vec{B} = ( (-1) * 3 - 1 * (-3) ) \ \hat{i} - ( 3 * 3 - 8 * (-3)) \ \hat{j} + (3 * 1 - 8 * (-1) ) \ \hat{k}](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%5Ctimes%20%20%5Cvec%7BB%7D%20%3D%20%28%20%28-1%29%20%2A%203%20-%201%20%2A%20%28-3%29%20%29%20%5C%20%20%5Chat%7Bi%7D%20-%20%28%203%20%2A%203%20-%208%20%2A%20%28-3%29%29%20%5C%20%5Chat%7Bj%7D%20%2B%20%283%20%2A%201%20-%208%20%2A%20%28-1%29%20%29%20%5C%20%5Chat%7Bk%7D)
![\vec{A} \times \vec{B} = ( - 3 + 3 ) \ \hat{i} - ( 9 + 24 ) \ \hat{j} + (3 + 8 ) \ \hat{k}](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%5Ctimes%20%20%5Cvec%7BB%7D%20%3D%20%28%20-%203%20%2B%203%20%29%20%5C%20%20%5Chat%7Bi%7D%20-%20%28%209%20%2B%2024%20%29%20%5C%20%5Chat%7Bj%7D%20%2B%20%283%20%2B%208%20%29%20%5C%20%5Chat%7Bk%7D)
![\vec{A} \times \vec{B} = 0 \ \hat{i} - 33 \ \hat{j} + 12 \ \hat{k}](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%5Ctimes%20%20%5Cvec%7BB%7D%20%3D%200%20%5C%20%20%5Chat%7Bi%7D%20-%2033%20%5C%20%5Chat%7Bj%7D%20%2B%2012%20%5C%20%5Chat%7Bk%7D)
![\vec{A} \times \vec{B} =(0, -33, 12)](https://tex.z-dn.net/?f=%5Cvec%7BA%7D%20%5Ctimes%20%20%5Cvec%7BB%7D%20%3D%280%2C%20-33%2C%2012%29)
<h2>B)</h2>
We know that
and
are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:
![|\vec{A} \times \vec{B} | = 2 * area_{triangle}](https://tex.z-dn.net/?f=%20%7C%5Cvec%7BA%7D%20%5Ctimes%20%20%5Cvec%7BB%7D%20%7C%20%3D%202%20%2A%20area_%7Btriangle%7D)
so:
![\sqrt{(-33)^2 + (12)^2} = 2 * area_{triangle}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28-33%29%5E2%20%2B%20%2812%29%5E2%7D%20%3D%202%20%2A%20area_%7Btriangle%7D)
![\sqrt{1233} = 2 * area_{triangle}](https://tex.z-dn.net/?f=%20%5Csqrt%7B1233%7D%20%3D%202%20%2A%20area_%7Btriangle%7D)
![35.114= 2 * area_{triangle}](https://tex.z-dn.net/?f=%2035.114%3D%202%20%2A%20area_%7Btriangle%7D)
![17.55 \ units \ of \ area = area_{triangle}](https://tex.z-dn.net/?f=%2017.55%20%5C%20units%20%5C%20%20of%20%5C%20area%20%3D%20%20area_%7Btriangle%7D)
Answer:
T’= 4/3 T
The new tension is 4/3 = 1.33 of the previous tension the answer e
Explanation:
For this problem let's use Newton's second law applied to each body
Body A
X axis
T = m_A a
Axis y
N- W_A = 0
Body B
Vertical axis
W_B - T = m_B a
In the reference system we have selected the direction to the right as positive, therefore the downward movement is also positive. The acceleration of the two bodies must be the same so that the rope cannot tension
We write the equations
T = m_A a
W_B –T = M_B a
We solve this system of equations
m_B g = (m_A + m_B) a
a = m_B / (m_A + m_B) g
In this initial case
m_A = M
m_B = M
a = M / (1 + 1) M g
a = ½ g
Let's find the tension
T = m_A a
T = M ½ g
T = ½ M g
Now we change the mass of the second block
m_B = 2M
a = 2M / (1 + 2) M g
a = 2/3 g
We seek tension for this case
T’= m_A a
T’= M 2/3 g
Let's look for the relationship between the tensions of the two cases
T’/ T = 2/3 M g / (½ M g)
T’/ T = 4/3
T’= 4/3 T
The new tension is 4/3 = 1.33 of the previous tension the answer e
V=d/t
V=?
d=400m(4)
=1600m
t=6 min.
=360 s
V=1600m/360s
V=4.4m/s