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AfilCa [17]
2 years ago
15

The magnitude of the velocity vector of the car is ∣∣v→∣∣ = 78 ft/s. If the vector v→ forms an angle θ = 0.09 rad with the horiz

ontal direction, determine the Cartesian representation of v→ relative to the (iˆ, jˆ) component system.
Physics
1 answer:
kotegsom [21]2 years ago
3 0

Answer:

\vec{v} = (77.68~{\rm ft/s})\^i + (7.01~{\rm ft/s})\^j

Explanation:

The x- and y- components of the velocity vector can be written as following:

\vec{v}_x = ||\vec{v}||\cos(\theta)\^i

\vec{v}_y = ||\vec{v}||\sin(\theta)\^j

Since the angle θ and the magnitude of the velocity is given, the vector representation can be written as follows:

\vec{v} = 78\cos(0.09)\^i + 78\sin(0.09)\^j\\\vec{v} = (77.68~{\rm ft/s})\^i + (7.01~{\rm ft/s})\^j

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rolling ball down a hill

Explanation:

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A 6.7kg object moves with a velocity of 8m/s. What's its kinetic energy?
Snezhnost [94]

Given parameters:

Mass of object = 6.7kg

Velocity  = 8m/s

Unknown parameter:

Kinetic energy  = ?

Energy is defined as the ability to do work. There are two forms of energy;

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Kinetic energy is the energy due to the motion of a body. Whereas, potential energy is the energy due to the position of a body usually at rest.

Kinetic energy is mathematically expressed as;

             Kinetic energy  = \frac{1}{2} m v^{2}

where m is the mass of the body

           v is the velocity of the body

Since we have been given both mass and velocity, input the parameter to solve for the unknown;

            Kinetic energy  = \frac{1}{2} x 6.7 x 8²   = 214.4‬J

So the kinetic energy of the body is  214.4‬J

3 0
3 years ago
A sample of argon gas (molar mass 40 g) is at four times the absolute temperature of a sample of hydrogen gas (molar mass 2 g).
qaws [65]

To solve this problem, let us recall that the formula for gases assuming ideal behaviour is given as:

rms = sqrt (3 R T / M)

where

R = gas constant = 8.314 Pa m^3 / mol K

T = temperature

M = molar mass

Now we get the ratios of rms of Argon (1) to hydrogen (2):

rms1 / rms2 = sqrt (3 R T1 / M1) / sqrt (3 R T2 / M2)

or

rms1 / rms2 = sqrt ((T1 / M1) / (T2 / M2))

rms1 / rms2 = sqrt (T1 M2 / T2 M1)

Since T1 = 4 T2

rms1 / rms2 = sqrt (4 T2 M2 / T2 M1)

rms1 / rms2 = sqrt (4 M2 / M1)

and M2 = 2 while M1 = 40

rms1 / rms2 = sqrt (4 * 2 / 40)

rms1 / rms2 = 0.447

 

Therefore the ratio of rms is:

<span>rms_Argon / rms_Hydrogen = 0.45</span>

7 0
3 years ago
A turtle takes 3.5 minutes to walk 18 m toward the south along a deserted highway. A truck driver stops and picks up the turtle.
Akimi4 [234]

Answer:

3.59 m/s

Explanation:

The average velocity is defined as:

\frac{Total displacement}{Total time}

The turtle first walks 18m south, and then is taken 1,1Km (or 1100m) north. Thus, the total displacement  is 1082m north (1100m north - 18m south).

Now we have to calculate the total time, which will be equal to the sum of the time the turtle walked and the time it was taken by truck.

The walking time is 3.5 minutes. Since 1 minute = 60 seconds, then the walking time is 210 seconds.

To calculate the truck time we use the equation:

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Thus,

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The total time is the sum of the walking time and the truck time.

Total time = 210s + 91.67s = 301.67s.

As mencioned previously, the average velocity is equal to total displacement/ total time, thus:

Average velocity = \frac{1082m}{301.67s} = 3.59 m/s North

Since the average velocity is a vector, it has a magnitude and a direction. In this case the magnitude is 3.59 m/s and the direction is north since the turtle's final displacement is north of where it started.

8 0
2 years ago
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