Physics, 19.03.2021 18:20 lightsofthedarkness

A 3.0-kilogram object initially at rest explodes and splits into three fragments. One fragment has a mass of 0.50 kg and flies off along the negative x axis at a speed of 2.8 m/s, and another has a mass of 1.3 kg and flies off along the negative y axis at a speed of 1.5 m/s. Required:
What are the speed and direction of the third fragment?

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Answer from: SKYBLUE1015

The speed and direction of the third fragment are 2 meters per second and 54.316º, respectively.

Explanation:

The object is not under the influence of any external force, meaning that Principle of Momentum Conservation to calculation of the velocity of the third fragment:

$(m_{1}+m_{2}+m_{3})\cdot \vec {v}_{o} = m_{1}\cdot \vec v_{1} + m_{2}\cdot \vec v_{2} + m_{3}\cdot \vec v_{3}$ (1)

Where:

$m_{1}$ , $m_{2}$ , $m_{3}$ - Masses of the first, second and third fragments, in kilograms.

$\vec v_{o}$ - Initial velocity of the object, in meters per second.

$\vec v_{1}$ , $\vec v_{2}$ , $\vec v_{3}$ - Velocities of the first, second and third fragments, in meters per second.

If we know that $m_{1} = 0.5\,kg$ , $m_{2} = 1.3\,kg$ , $m_{3} = 1.2\,kg$ , $\vec v_{o} = (0,0)\,\left[\frac{m}{s} \right]$ , $\vec v_{1} = \left(-2.8, 0\right)\,\left[\frac{m}{s} \right]$ and $\vec v_{2} = \left(0,-1.5\right)\,\left[\frac{m}{s} \right]$ , the velocity of the third fragment is:

$(-1.4,0) + (0,-1.95) + 1.2\cdot \vec v_{3} = (0,0)$

$1.2\cdot \vec v_{3} = (1.4,1.95)$

$\vec v_{3} = (1.167, 1.625)\,\left[\frac{m}{s} \right]$

The speed of the third fragment is the magnitude of the result found above:

$v_{3} = 2\,\frac{m}{s}$

And the direction of the third fragment is:

$\theta_{3} = \tan^{-1} \left(\frac{1.625}{1.167}\right)$

$\theta_{3} \approx 54.316^{\circ}$

The speed and direction of the third fragment are 2 meters per second and 54.316º, respectively.

Answer from: Quest

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.

Answer from: Quest

it's when something is going so fast it makes a loud noise, breaking the sound barrier, for example: a jet makes a loud noise, not only cause of the jet but because they reached a point where they went so fast that you can year the noise from various parts, kinda like a police car, lets say the car was going so fast that you hear the siren of the cop car right next to you, but the car is probably a mile a way, it's cos the siren was next to you a few seconds if you understand me

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A 3.0-kilogram object initially at rest explodes and splits into three fragments. One fragment has a...

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