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3 years ago

Which of the following is the dot product of u = 4i + 6j – 5k and v=-10i – 8j + 10k?

Physics

1 answer:

SVETLANKA909090 [29]3 years ago

7 0

Answer:

$\vec u\ . \ \vec v=-138$

Explanation:

Dot Product of Vectors

The dot product of two vectors is also known as scalar product. Given the vectors

$\vec u=4\hat i+6\hat j-5\hat k$

$\vec v=-10\hat i-8\hat j+10\hat k$

The dot product is the sum of the products of each component separately

$\vec u\ . \ \vec v=(4)(-10)+(6)(-8)+(-5)(10)$

$\vec u\ . \ \vec v=-40-48-50=-138$

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Two ice skaters stand together as illustrated in the attached figure. They "push off" and travel directly away from each other,

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By definition, the momentum is given by:
p = m * v
Where,
m = mass
v = speed.
On the other hand,
F = m * a
Where,
m = mass
a = acceleration:
For the boy we have:
p1 = m * v
p1 = (F / a) * v
p1 = ((710) / (9.81)) * (0.50)
p1 = 36.19 Kg * (m / s)
For the girl we have:
p2 = m * v
p2 = (F / a) * v
p2 = ((480) / (9.81)) * (v)
p2 = 48.93 * v Kg * (m / s)
Then, we have:
p1 + p2 = 0
36.19 + 48.93 * v = 0
Clearing v:
v = - (36.19) / (48.93)
v = -0.74 m / s (negative because the velocity is in the opposite direction of the boy's)
Answer:
the girl's velocity in m / s after they push off is -0.74 m / s

6 0

3 years ago

A 1.5-kg block slides at rest starts sliding down a snow-covered hill Point A, which has an altitude of 10 m. There is no fricti

damaskus [11]

Answer:

the speed of the block when it reaches point B is 14 m/s

Explanation:

Given that:

mass of the block slides = 1.5 - kg

height = 10 m

Force constant = 200 N/m

distance of rough surface patch = 20 m

coefficient of kinetic friction = 0.15

In order to determine the speed of the block when it reaches point B.

We consider the equation for the energy conservation in the system which can be represented by:

$\dfrac{1}{2}mv^2=mgh$

$\dfrac{1}{2}v^2=gh$

$v^2=2 \times g \times h$

$v^2=2 \times 9.8 \times 10$

$v=\sqrt{2 \times 9.8 \times 10$

$v=\sqrt{196$

v = 14 m/s

Thus; the speed of the block when it reaches point B is 14 m/s

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3 years ago

A ball is thrown horizontally from the top of a building 22.3 m high. The ball strikes the ground at a point 127 m from the base

DochEvi [55]

Answer:

t = 2.13 s

Explanation:

given,

height of the building = 22.3 m

horizontal distance = 127 m

acceleration due to gravity = 9.8 m/s²

time for which ball is in motion = ?

using equation of motion

$s = u t + \dfrac{1}{2}gt^2$

initial velocity is zero

$s = \dfrac{1}{2}gt^2$

$t = \sqrt{\dfrac{2s}{g}}$

$t = \sqrt{\dfrac{2\times 22.3}{9.8}}$

t = √4.551

t = 2.13 s

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3 years ago

What is the speed of light with N=1.33

alexgriva [62]

If the refractive index of some substance is 1.33, then
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 (speed of light in vacuum) / (1.33) =

 (299,792,458 m/s) / (1.33) = 225,407,863 m/s

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3 years ago

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A plank rests on top of the axles of two identical wheels. Each wheel's outer radius is 0.25 meters and each wheel's axle has ra

kaheart [24]

Answer:

The plank moves 0.2m from it's original position

Explanation:

we can do this question from the constraints that ,