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notka56 [123]
3 years ago
12

You are given a vector A = 125i and an unknown vector B that is perpendicular to A. The cross-product of these two vectors is A

× B = 98k.
What is the y-component of vector B?
Physics
1 answer:
Elena L [17]3 years ago
4 0

Answer:

  B_{y} = 0.784

Explanation:

The vector product of two vectors is

      A = Aₓ i ^ + A_{y} j ^

      B = Bₓ i ^ + B_{y} j ^

the cross product is

    A xB = \left[\begin{array}{ccc}i&j&k\\A_{x}&A_{y}&0\\B_{x}&B_{y}&0\end{array}\right]

   A x B =i^   + j^    + k^ (Aₓ B_{y} + A_{y} Bₓ)

     

is the result they give is

       A x B = 98 k ^

           

tells us that Aₓ = 125, we substitute

       98 = 125 B_{y} - Bₓ 0

       B_{y} = 98/125

       B_{y} = 0.784

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Sunny_sXe [5.5K]

Answer:

The speed of the car at the apex of the loop must be grater than 2.45 m/s

Explanation:

In order for the car to not fall off the track at the apex of the loop, the norm force of the track at the apex must be greater than zero.

Assuming frictionless life on the track which is also to have a perfectly circular shape near the top (radius being 0.25m), the norm force of the track and gravity both point down and result in the centripetal force:

F_c=F_N+F_g

The formula for centripetal force on a circular trajectory is

F_c = m\frac{v^2}{r}

and so the condition for the car to stay on the track can be written as

m\frac{v^2}{r} = F_N + mg\implies F_N = m\frac{v^2}{r}-mg>0\\\implies |v| >\sqrt{gr}=\sqrt{9.8\frac{m}{s^2}0.25m}=2.45\frac{m}{s}

The speed of the car at the apex of the loop must be grater than 2.45 m/s


3 0
3 years ago
Um automóvel percorre 6,0 km para o norte e, em seguida 8,0 km para o leste. A intensidade do vetor posição, em relação ao ponto
Valentin [98]

Answer:

Explanation:

A car travels 6.0 km to the north and then 8.0 km to the east. The intensity of the position vector, in relation to the starting point is: a) 14 km b) 2.0 km c) 12 km d) 10 km e) 8.0 km

Check attachment for diagram

The intensity of the position vector is equal to the displacement,

So, to calculate the displacement, we need to find the length of the straight line from starting point to end point.

So, applying Pythagorean theorem

c² = a² + b²

R² = 6² + 36²

R² = 36 + 64

R² = 100

R = √100

R = 10 km.

Verifique el adjunto para ver el diagrama

La intensidad del vector de posición es igual al desplazamiento,

Entonces, para calcular el desplazamiento, necesitamos encontrar la longitud de la línea recta desde el punto inicial hasta el punto final.

Entonces, aplicando el teorema de Pitágoras

c² = a² + b²

R² = 6² + 36²

R² = 36 + 64

R² = 100

R = √100

R = 10 km.

7 0
4 years ago
A golf ball stays on the tee until the golf club hits it. Which of the following principles best describes why this occurs? A) N
wel

Answer:

C) Newton's law of inertia

Explanation:

The law states that a body will continue in its state of rest or uniform motion unless compel by some external forces (acted upon by an unbalanced force) to act otherwise. In this case the golf will remain in it state because the downward force of gravity is equal to the upward force of normal and the horizontal vector sum of the forces acting on the body is zero.

3 0
3 years ago
A tall cylinder contains 25 cm of water. Oil is carefully poured into the cylinder, where it floats on top of the water, until t
Fed [463]

Answer: 377.3\ kPa

Explanation:

Given

Water column height h=25\ cm

After oil is poured, the total height becomes h'=40\ cm

Pressure at the bottom will be the sum due to the water and oil column

Suppose the density of the oil is \rho=900\ kg/m^3

Pressure at the bottom

\Rightarrow P=10^3\times g\times 25+900\times g\times 15\\\Rightarrow P=100g[250+135]\\\Rightarrow P=3773\times 100\ Pa\\\Rightarrow P=377.3\ kPa

4 0
3 years ago
8. A boy pulls a 20.0-kg box with a 140-N force at 30° above a horizontal surface. If the coefficient of kinetic friction betwee
LenaWriter [7]

0.280 m is the correct answer

8 0
3 years ago
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