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Nutka1998 [239]
3 years ago
5

The vertical motion of mass A is defined by the relation x 5 10 sin 2t 1 15 cos 2t 1 100, where x and t are expressed in millime

ters and seconds, respectively. Determine (a) the position, velocity, and acceleration of A when t 5 1 s, (b) the maximum velocity and acceleration of A.
Physics
1 answer:
nikklg [1K]3 years ago
5 0

Explanation:

Given that,

The vertical motion of mass A is defined by the relation as :

x=10\ sin2t+15\ cos2t+100

At t = 1 s

x=10\ sin2+15\ cos2+100

x = 115.33 mm

(a) We know that,

Velocity, v=\dfrac{dx}{dt}

v=\dfrac{d(10\ sin2t+15\ cos2t+100)}{dt}

v=20\ cos2t-30\ sin2t

At t = 1 s

v=20\ cos2-30\ sin2

v = 18.94 mm/s

We know that,

Acceleration, a=\dfrac{dv}{dt}

a=\dfrac{d(20\ cos2-30\ sin2)}{dt}

a=-40\ cos2t-60\ cos2t

At t = 1 s

v=-40\ cos2-60\ cos2

a=-99.93\ mm/s^2

(b) For maximum velocity, \dfrac{dv}{dt}=a=0

-40\ cos2t-60\ cos2t=0

t = 45 seconds

For maximum acceleration, \dfrac{da}{dt}=0

80\ sin2t+120\ cos2t=0

t = 61.8 seconds

Hence, this is the required solution.

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A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound
Strike441 [17]

Answer:

5.997m/s

Explanation:

We were told to calculate the speed of the ball,

Given speed of sound as 340 m

And we know that the sound of the ball hitting the pins is at 2.80 s after the ball is released from his hands.

Speed of ball = distance traveled/(time of hearing - time the sound travels).

Speed= S/t

Where S= distance traveled

t= time of hearing - time the sound travels

time=time for ball to roll+timefor sound to come back.

time of sound=16.5/340

=0.048529secs

solving for speedof ball

Then,Speed of ball = distance traveled/(time of hearing - time the sound travels).

=16.5/(2.80-0.048529) m/s = 5.997m/s

Therefore, the speed of the ball is

5.997m/s

4 0
2 years ago
Answer the following question: “Do the particles in a gas ever slow down and stop? Include information about the three states of
jarptica [38.1K]

Answer:

I hope it is no too late

Explanation:

hmmm,

In a gas, for example, the molecules are traveling in random directions at a variety of speeds - some are fast and some are slow. ... If more energy is put into the system, the average speed of the molecules will increase and more thermal energy or heat will be produced.

3 0
3 years ago
A bicycle pump contains 20 cm3 of air at a pressure of 100 kPa. The air is then pumped in a tyre of volume 100 cm3. Calculate th
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Answer:

The pressure of the air in the tyre is 20 kPa

Explanation:

The parameters for the bicycle pump and tyre are;

The volume of air contained in the bicycle pump, V₁ = 20 cm³

The pressure of the air contained in the bicycle pump, P₁ = 100 kPa

The volume (available) of the tyre, where the air is pumped, V₂ = 100 cm³

Let P₂ represent the pressure in the tyre after the air is pumped

By Boyle's law, we have that at constant temperature, the volume of a given mass of gas is inversely proportional to its pressure;

Mathematically, Boyle's law gives the following equation;

P₁ × V₁ = P₂ × V₂

∴ P₂ = (P₁ × V₁)/V₂

Substituting the known values gives;

P₂ = (100 kPa × 20 cm³)/(100 cm³)

∴ P₂ = 100 kPa × 1/5 = 20 kPa

P₂ = 20 kPa

The pressure of the air in the tyre = P₂ = 20 kPa.

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The sun can continue to exist in its present stable state for about another
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Answer:

5.5 billion years

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The answer

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