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1 year ago

Determine the value of n so that the vectors A and B are perpendicular: Ā = î + 5j + nk and B = 2î - j + k

Physics

1 answer:

Tanya [424]1 year ago

6 0

If $\vec A$ and $\vec B$ are perpendicular, then their dot product is zero. This means

$\vec A \cdot \vec B = (\vec\imath + 5\,\vec\jmath + n\,\vec k) \cdot (2\,\vec\imath - \vec\jmath + \vec k) = 2 - 5 + n = 0$

Solving for n is trivial; it follows that n = 3.

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A car is traveling at 30 m/s in a straight line. The drive applies the brakes for 3 seconds and the car slows down to 12 m/s. Wh

jeyben [28]

Answer:

The answer to your question is: -6m/s²

Explanation:

Data

vo = 30 m/s

vf = 12 m/s

t = 3 s

a = ?

Formula

vf = vo + at

a = (vt - vo) / t

Process

a = (12 - 30) / 3 substitution

a = -18 / 3 simplify

a = -6 m/s² result, is negative because the car

is slowing down.

3 0

3 years ago

A boy takes hold of a rope to pull a wagon (m = 50 kg) on a surface with a static coefficient of friction μS = 0.25. Calculate t

vivado [14]

Answer:

<em>The force that would be applied on the rope just to start moving the wagon is 122 N</em>

Explanation:

Frictional force opposes motion between two surfaces in contact. It is the force that must be applied before a body starts to move. Static friction opposes the motion of two bodies that are in contact but are not moving. The magnitude of static friction to overcome for the body to move can be calculated using equation 1.

F = μ x mg .............................. 1

where F is the frictional force;

μ is the coefficient of friction ( μs, in this case, static friction);

m is mass of the object and;

g is the acceleration due to gravity( a constant equal to 9.81 m/ $s^{2}$ )

from the equation we are provide with;

μs = 0.25

m = 50 kg

g = 9.81 m/ $s^{2}$

F =?

Using equation 1

F = 0.25 x 50 kg x 9.81 m/ $s^{2}$

F = 122.63 N

<em>Therefore a force of 122 N must be applied to the rope just to start the wagon.</em>

6 0

3 years ago

Read 2 more answers

A boat takes 3.0 hours to travel 50 km down a river, then 5.4 hours to return. Determine the speed of the water in the river.

Nutka1998 [239]

Answer:

3.7 km/h

Explanation:

Let's call v the proper speed of the boat and v' the speed of the water in the river.

When the boat travels in the direction of the current, the speed of the boat is:

v + v'

And it covers 50 km in 3 h, so we can write

$v+v' = \frac{50 km}{3 h}=16.7 km/h$ (1)

When the boat travels in the opposite direction, the speed of the boat is

v - v'

And it covers 50 km in 5.4 h, so

$v-v'=\frac{50 km}{5.4 h}=9.3 km/h$ (2)

So we have a system of two equations: by solving them simultaneously, we find the value of v and v':

$v+v'=16.7 \\v-v'=9.3$

Subtracting the second equation from the first one we get:

$(v+v')-(v-v')=16.7-9.3\\2v'=7.4\\v'=3.7$

So, the speed of the water is 3.7 km/h.

5 0

3 years ago

John goes grocery shopping with his mother. His job is to push the cart. The cart is

lora16 [44]

Answer:

Beacause he has more grocceries and food heavy

Explanation:

7 0

2 years ago

Two asteroids identical to those above collide at right angles and stick together; i.e, their initial velocities were perpendicu

11111nata11111 [884]

Answer:

velocity = 62.89 m/s in 58 degree measured from the x-axis

Explanation:

Relevant information:

Before the collision, asteroid A of mass 1,000 kg moved at 100 m/s, and asteroid B of mass 2,000 kg moved at 80 m/s.

Two asteroids moving with velocities collide at right angles and stick together. Asteroid A initially moving to right direction and asteroid B initially move in the upward direction.

Before collision Momentum of A = 1000 x 100 = $10^5$ kg - m/s in the right direction.