Answer:
In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
Answer:0.507m
To answer this question, you need to know how to calculate a cube volume. Cube volume is calculated by multiplying the length^3, make its unit become cubic meter.
In this case we know the volume is 130L and asked how long is the length in meter. Then you need to convert the liter into m3. The calculation would be:
V=R^3
130L= R^3
R= 3<span>√(130m3/1000)
R= 5.065797/10 m
R= 0.506579m
Rounded up to 0.507m</span>
Answer:
The maximum height the pumpkin reaches occurs at 62.5 horizontal meters from its launching spot.
Explanation:
Notice that we are given the actual trajectory equation:
![y=-0.008 \, x^2+x](https://tex.z-dn.net/?f=y%3D-0.008%20%5C%2C%20x%5E2%2Bx)
which corresponds to a curve represented by a parabola.
We can find the maximum of this parabola with arms pointing down requesting the derivative (slope of the tangent line to the curve) to be zero :
![y'=-0.016\,x+1\\0=-0.016x+1\\x=\frac{1}{0.016} \\x=62.5\,\,m](https://tex.z-dn.net/?f=y%27%3D-0.016%5C%2Cx%2B1%5C%5C0%3D-0.016x%2B1%5C%5Cx%3D%5Cfrac%7B1%7D%7B0.016%7D%20%5C%5Cx%3D62.5%5C%2C%5C%2Cm)
The potential energy of a mass is given by the formula:
![E_p=m\cdot g\cdot h](https://tex.z-dn.net/?f=E_p%3Dm%5Ccdot%20g%5Ccdot%20h)
Where m is the mass, g is the gravity acceleration and h is the height.
Since the mass and gravity will be constant, for half the potential energy, we have:
![\begin{gathered} E^{\prime}_p=m\cdot g\cdot h^{\prime} \\ E^{\prime}_p=\frac{E_p}{2} \\ \\ m\cdot g\cdot h^{\prime}=\frac{m\cdot g\cdot h}{2} \\ h^{\prime}=\frac{h}{2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20E%5E%7B%5Cprime%7D_p%3Dm%5Ccdot%20g%5Ccdot%20h%5E%7B%5Cprime%7D%20%5C%5C%20E%5E%7B%5Cprime%7D_p%3D%5Cfrac%7BE_p%7D%7B2%7D%20%5C%5C%20%20%5C%5C%20m%5Ccdot%20g%5Ccdot%20h%5E%7B%5Cprime%7D%3D%5Cfrac%7Bm%5Ccdot%20g%5Ccdot%20h%7D%7B2%7D%20%5C%5C%20h%5E%7B%5Cprime%7D%3D%5Cfrac%7Bh%7D%7B2%7D%20%5Cend%7Bgathered%7D)
So the box will have half the potential energy at half the height of the ramp.
The effective length of the tube is responsible for determining the frequency of vibration of the air column in the tube within a wind instrument.