A. Do the waves made by the two faucets travel faster than the waves made by just one faucet?

Planet X has three times the free-fall acceleration of Earth.

serious [3.7K]

Answer:

a) The ball goes one-third times higher on X

b) The ball goes three times higher on X.

Explanation:

a)

As the initial velocity is the same than on Earth, but the free-fall acceleration is three times larger, this means that the only net force acting on the ball (gravity) will be three times larger, so it is clear that the ball will reach to a lower height, as it will slowed down more quickly.
Kinematically, as we know that the speed becomes zero when the ball reaches to the maximum height, we can use the following kinematic equation:

$v_{f} ^{2} - v_{o}^{2} = 2* \Delta h* g$

since vf = 0, solving for Δh, we have:

$\Delta h = h_{max} =\frac{v_{o} ^{2}}{2*g} (1)$

if v₀ₓ = v₀E, and gₓ = 3*gE, replacing in (1), we get:

Δhₓ = 1/3 * ΔhE

which confirms our intuitive reasoning.

b)

Now, if the initial velocity is three times larger than the one on Earth, even the acceleration due to gravity is three times larger, we conclude that the ball will go higher than on Earth.
We can use the same kinematic equation as in (1) replacing Vox by 3*VoE, as follows:

$\Delta h = h_{max} =\frac{(3*v_{o}) ^{2}}{2*3*g} (2)$

Replacing the right side of (1) in (2), we get:

Δhx = 3* ΔhE

which confirms our intuitive reasoning also.

7 0

3 years ago

A 1.65 kg mass stretches a vertical spring 0.260 m If the spring is stretched an additional 0.130 m and released, how long does

Irina-Kira [14]

Answer:

The system will take approximately 0.255 seconds to reach the (new) equilibrium position.

Explanation:

We notice that block-spring system depicts a Simple Harmonic Motion, whose equation of motion is:

$y(t) = A\cdot \cos \left(\sqrt{\frac{k}{m} }\cdot t +\phi\right)$ (1)

Where:

$y(t)$ - Position of the mass as a function of time, measured in meters.

$A$ - Amplitude, measured in meters.

$k$ - Spring constant, measured in newtons per meter.

$m$ - Mass of the block, measured in kilograms.

$t$ - Time, measured in seconds.

$\phi$ - Phase, measured in radians.

The spring is now calculated by Hooke's Law, that is:

$k = \frac{m\cdot g}{\Delta y}$ (2)

Where:

$g$ - Gravitational acceleration, measured in meters per square second.

$\Delta y$ - Deformation of the spring due to gravity, measured in meters.

If we know that $m=1.65\,kg$ , $g = 9.807\,\frac{m}{s^{2}}$ and $\Delta y = 0.260\,m$ , then the spring constant is:

$k = \frac{(1.65\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{0.260\,m}$

$k = 62.237\,\frac{N}{m}$

If we know that $A = 0.130\,m$ , $k = 62.237\,\frac{N}{m}$ , $m=1.65\,kg$ , $x(t) = 0\,m$ and $\phi = 0\,rad$ , then (1) is reduced into this form:

$0.130\cdot \cos (6.142\cdot t)=0$ (1)

And now we solve for $t$ . Given that cosine is a periodic function, we are only interested in the least value of $t$ such that mass reaches equilibrium position. Then:

$\cos (6.142\cdot t) = 0$

$6.142\cdot t = \cos^{-1} 0$

$t = \frac{1}{6.142}\cdot \left(\frac{\pi}{2} \right)\,s$

$t \approx 0.255\,s$

The system will take approximately 0.255 seconds to reach the (new) equilibrium position.

4 0

3 years ago

A sound wave is often called a pressure wave because there are regions of high and low pressure established in them medium throu

Bingel [31]

Explanation:

A sound wave is often called a pressure wave because there are regions of high and low pressure established in them medium through which the sound wave travels. The regions of high pressure are known as Compressions and the regions of low pressure are known as Rarefactions . Sound waves are composed of compressions and rarefactions. Compressions are the parts where the molecules are congusted and pressed together. However in the rarefactions molecules are relax and have enough space for expansion. Sound waves are the logitudnal waves and always been defined as the motion of the medium particles parallel to the wave motion.

7 0

3 years ago

You drive a car for 2.0 h at 60 km/h, then for another 3.0 h at 85 km/h. What is your average velocity

Anon25 [30]

Answer:

Explanation:

Average velocity is found in the total displacement experienced in the trip divided by the total time it took to make this trip. If, for the first 2.0 hours, the car travels at 60 km/hr, then in 2.0 hours the car can travel 120 km; if it then travels for 3.0 at 85 km/hr, it can travel 255 km in the same direction. The total time this took was 5.0 hours. So doing the math and rounding correctly by following the rules for the adding and subtracting of sig fig's:

$v=\frac{120+255}{5.0}=\frac{380}{5.0}=76\frac{km}{hr}$

If you do not round when you add, the average velocity is 75 km/hr

8 0

3 years ago

The Sun's declination is 0° at the _________. A. summer and winter solstice B. summer and winter equinox C. vernal and autumnal

Olegator [25]

-- "Declination zero" means the object is in the sky at some point directly over the Earth's equator.

-- If it's the sun and it appears to be over the equator, then that tells us that the Earth's axis is not tilted toward or away from it.

-- That in turn tells us that the Earth is at one of the two equinoxes in its orbit, either the Spring one or the Autumn one. (D)

-- (The first days of Summer and Winter coincide with solstices, not equinoxes.)

5 0

3 years ago

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