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2 years ago

The equation y = 5 Sin (3x - 4t), where

Physics

1 answer:

igomit [66]2 years ago

4 0

Answer:

Frequency, f = 0.63 Hz

Period, T = 1.58 s

Speed of a wave, v = 1.34 m/s

Explanation:

The equation of a wave is given by :

$y = 5 \sin (3x - 4t)$ ...(1)

y is in mm

x is in meters

t is in seconds

The general equation of a wave is given by :

$y=A\sin(kx-\omega t)$ ...(2)

(i) Compare equation (1) and (2) we get :

$k=3\\\\\omega=4$

Since,

$\omega=2\pi f\\\\f=\dfrac{\omega}{2\pi}\\\\f=\dfrac{4}{2\pi}\\\\f=0.63\ Hz$

(ii) Period of wave is :

$T=\dfrac{1}{f}\\\\T=\dfrac{1}{0.63}\\\\T=1.58\ s$

(iii) Speed of a wave,

$v=\dfrac{\omega}{k}\\\\v=\dfrac{4}{3}\\\\v=1.34\ m/s$

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A player kicks a football from ground level with a velocity of 26.2m/s at an angle of 34.2° above the horizontal. How far back f

Amanda [17]

For the ball to go straight into the goal, the kicker needs to be no more than 6.54 meters away from the goal.

For the ball to arc into the goal, the kicker needs to be between 58.5 and 65.1 meters away from the goal.

<h3>Explanation</h3>

How long does it take for the ball to reach the goal?

Let the distance between the kicker and the goal be $x$ meters.

Horizontal velocity of the ball will always be $26.2\times\cos{34.2\textdegree}$ until it lands if there's no air resistance.

The ball will arrive at the goal in $\displaystyle \frac{x}{26.2\times\cos{34.2\textdegree}}$ seconds after it leaves the kicker.

What will be the height of the ball when it reaches the goal?

Consider the equation

$\displaystyle h(t) = -\frac{1}{2}\cdot g\cdot t^{2} + v_{0,\;\text{vertical}} \cdot t + h_0$ .

For this soccer ball:

$g = 9.81\;\text{m}\cdot\text{s}^{-2}$ ,
$v_{0,\;\text{vertical}} = 26.2\times \sin{34.2\textdegree{}}\;\text{m}\cdot\text{s}^{-2}$ ,
$h_0 = 0$ since the player kicks the ball "from ground level."

$\displaystyle t=\frac{x}{26.2\times\cos{34.2\textdegree}}$

when the ball reaches the goal.

$\displaystyle h= - 9.81 \times \frac{x^2}{(26.2\times\cos{34.2\textdegree})^2} + (26.2 \times \sin{34.2\textdegree})\times\frac{x}{26.2\times\cos{34.2\textdegree}} \\\phantom{h} = -\frac{9.81}{(26.2\times\cos{34.2\textdegree})^2}\cdot x^{2} + \frac{\sin{34.2\textdegree}}{\cos{34.2\textdegree}}\cdot x$ .

Solve this quadratic equation for $x$ , $x > 0$ .

$x = 65.1$ meters when $h = 0$ meters.
$x = 6.54$ or $58.5$ meters when $h = 4$ meters.

In other words,

For the ball to go straight into the goal, the kicker needs to be no more than 6.54 meters away from the goal.
For the ball to arc into the goal, the kicker needs to be between 58.5 and 65.1 meters away from the goal.

3 0

2 years ago

How long will your trip take if you travel 4000 m at an average speed of 8m/s

SpyIntel [72]

Answer:

500 sec

8 min 20 sec

Explanation:

Hi there !

8 m ................ 1 s

4000 m ........ x s

x = 4000m×1s/8m = 500 sec = 8 min 20 sec

Good luck !

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2 years ago

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A fairgrounds ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follo

cestrela7 [59]

Answer:

13.37 rev/min

Explanation:

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r = 9 m

Centripetal acceleration ( $a_c$ ) is given by:

$a_c=\frac{v^2}{r} \\\\v=\sqrt{a_c*r} \\\\v=\sqrt{17.64\ m/s^2*9\ m}\\\\v=12.6\ m/s$

The velocity (v) is given by:

v = ωr; where ω is the angular velocity

Hence:

ω = v/r = 12.6 / 9

ω = 1.4 rad/s

ω = 2πN

N = ω/2π = 1.4 / 2π

N = 0.2228 rev/s

N = 13.37 rev/min

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2 years ago

Roseanne heated a solution in a beaker as part of a laboratory experiment on energy transfer. After a while, she noticed the liq

sveta [45]

I think it is convection hope I could help.

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3 years ago

Lee pushes horizontally with a force of 75 n on a 36 kg mass for 10 m across a floor. calculate the amount of work lee did. answ

svlad2 [7]

To find work, you use the equation: W = Force X Distance X Cos (0 degrees)
Following the Law of Conservation of Energy, energy cannot be destroyed nor created.

So you would do 75 N x 10m x Cos (0 degrees)= 750 J

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2 years ago

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