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Paladinen [302]
3 years ago
11

A particle is moving with SHM of period pie . initially it is 10 cm from The center of the motion and moving in the positive dir

ection with speed of 6cm/s find an equation to describe motion
Physics
1 answer:
Viefleur [7K]3 years ago
7 0

Answer:

y = 10.44cos(2t - 0.291) cm

Explanation:

y = Acos(2πt/T + φ) = Acos(2πt/π + φ) = Acos(2t + φ)

v = y' = -2Αsin(2t + φ)

10 = Acos(2(0) + φ) = Acosφ

6 = -2Αsin(2(0) + φ) = -2Asinφ

6/10 = -2Asinφ/Acosφ = -2tanφ

tanφ = -0.3

φ = -0.291 radians

10 = Acos(-0.291)

A = 10/cos(-0.291) = 10.44

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A police officer is parked by the side of the road, when a speeding car travelling at 50 mi/hrpasses. The police car immediately
Blababa [14]

Answer:

a) time taken to catch up with speeding car is 12.25 secs

b) the police car will travel 273.8 m to catch up with the speeding car

Explanation:

Given that;

speed of car V_{c} = 50 mi/hr = 22.352 m/s

acceleration of police car = 10 mi/hr = 4.47 m/s²

V_{f}  = 70 mi/hr = 31.29 m/s

Now time taken to reach maximum speed is t₁

so

V_{f} =  V_{i} + at₁

we substitute

31.29 = 0 + 4.47t₁

t₁ = 31.29 / 4.47

t₁  = 7 sec

now

d₁ = 0 + 1/2 × at₁²

d₁ = 0 + 1/2 × 0 + 4.47×(7)²

d₁ = 109.5 m

so distance travelled by the speeding car in time t₁  will be

d_{c} = V_{c} × t₁

we substitute

d_{c} = 22.352 × 7

d_{c}  = 156.46 m

now distance between polive car and speeding car

Δd =  d_{c} - d₁

Δd = 156.46 - 109.5

Δd = 46.96 m

time taken to cover Δd will be

t₂ = Δd / ( V_{f} - V_{c} )

t₂ = 46.96 / ( 31.29 - 22.352 )

t₂ = 46.96 / 8.938

t₂ = 5.25 sec

distance travelled by the police in time t₂ will be

d₂ = V_{f} × t₂

d₂ = 31.29 × 5.25

d₂ = 164.3 m

a) How long will it take before the officer catches up to the speeding car;

time taken to catch up with speeding car;

t = t₁ + t₂

t = 7 + 5.25

t = 12.25 secs

Therefore, time taken to catch up with speeding car is 12.25 secs

b)  how far will it have travelled in order to do so;

distance = d₁ + d₂

distance = 109.5 + 164.3

distance = 273.8 m

Therefore, the police car will travel 273.8 m to catch up with the speeding car

6 0
3 years ago
A lead ball has a mass of 55.0 grams and a density of 11.4 g/cm3. what is the volume of the ball?
lesantik [10]
Density=mass/volume therefore volume=mass/density; 55g/11.4g/cm^3= 4.82cm^3
6 0
3 years ago
Read 2 more answers
When light propagates from a material with a given index of refraction into a material with a smaller index of refraction, the s
SSSSS [86.1K]

Answer: A) increase

Explanation:

7 0
3 years ago
The period of rotation of Mars is 1 day and 37 minutes. Determine its frequency of rotation in Hertz.
Sholpan [36]

The frequency of rotation of Mars is 0.0000113 Hertz.

<u>Given the following data:</u>

  • Period = 1 day and 37 minutes.

To find the frequency of rotation in Hertz:

First of all, we would convert the the value of period in days and minutes to seconds because the period of oscillation of a physical object is measured in seconds.

<u>Conversion:</u>

1 day = 24 hours

24 hours to minutes = 60 × 24 = 1440 minutes

1440 + 37 = 1477 \; minutes

1 minute = 60 seconds

1477 minute = X seconds

Cross-multiplying, we have:

X = 60 × 1477

X = 88620 seconds

Now, we can find the frequency of rotation of Mars by using the formula:

Frequency = \frac{1}{Period}\\\\Frequency = \frac{1}{88620}

<em>Frequency </em><em>of rotation</em> = <em>0.0000113 Hertz</em>

Therefore, the frequency of rotation of Mars is 0.0000113 Hertz.

Read more: brainly.com/question/14708169

8 0
3 years ago
The speed of light in air is 3 x 108 m/s. The speed of light in ice is 2.29 x 108 m/s. What is the refractive index from air to
Studentka2010 [4]

Answer:

η = 1.31

Explanation:

The formula for the refractive index of from air to some other medium is given by the following formula:

\eta = \frac{c}{v}\\

where,

η = refractive index = ?

c = speed of light in air = 3 x 10⁸ m/s

v = speed of light in ice = 2.29 x 10⁸ m/s

Therefore, using these values in the equation we get:

\eta = \frac{3\ x\ 10^8\ m/s}{2.29\ x\ 10^8\ m/s} \\

<u>η = 1.31</u>

4 0
2 years ago
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