Jane's mechanical energy at any time is
![E=U+K](https://tex.z-dn.net/?f=E%3DU%2BK)
where
![U=mgh](https://tex.z-dn.net/?f=U%3Dmgh)
is the potential energy, while
![K= \frac{1}{2} mv^2](https://tex.z-dn.net/?f=K%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
is the kinetic energy.
Initially, Jane is on the ground, so the altitude is h=0 and the potential energy is zero: U=0. She's running with speed v, so she has kinetic energy only:
![E=K= \frac{1}{2} mv^2](https://tex.z-dn.net/?f=E%3DK%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
Then she grabs the vine, and when she reaches the maximum height h, her speed is zero: v=0, and so the kinetic energy becomes zero: K=0. So now her mechanical energy is just potential energy:
![E=U=mgh](https://tex.z-dn.net/?f=E%3DU%3Dmgh)
But E must be conserved, so the initial kinetic energy must be equal to the final potential energy:
![\frac{1}{2}mv^2=mgh](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%3Dmgh%20)
from which we can find h, the maximum height Jane can reach:
The answer is: by using evidence from many investigations
Density- It is a measurement of that how material is packed together tightly.
Its formula is ρ=m/v
where ρ is the density of material
m is the mass
v is the volume
here we have to find the length of cube's side
a cube of silver has a mass = 21 kg. = 21×10³ [∵1kg = 1000g ]
density of silver = 10.49g/cm³
the length of the cube's side = ?
v=m/ρ
l³ = 21×10³ /10.49 ≈ 2×10³ cm³
l =∛(2×10³)cm³
l = 1.26 ×10 = 12.6 cm
l = 4.96 inches [∵ 1 cm = 0.394 inch ]
the length of the cube's side is 4.96 inches
to know more about density :
brainly.com/question/10847047
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Answer:
275 kPa
Explanation:
mass of the gas=m=1.5 kg
initial volume if the gas=V₁=0.04 m³
initial pressure of the gas= P₁=550 kPa
as the condition is given final volume is double the initial volume
V₂=final volume
V₂=2 V₁
As the temperature is constant
T₁=T₂=T
=![\frac{P2 V2}{T2}](https://tex.z-dn.net/?f=%5Cfrac%7BP2%20V2%7D%7BT2%7D)
putting the values in the equation.
=![\frac{P2 *2V1}{T2}](https://tex.z-dn.net/?f=%5Cfrac%7BP2%20%2A2V1%7D%7BT2%7D)
P₂=![\frac{P1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7BP1%7D%7B2%7D)
P₂=![\frac{550}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B550%7D%7B2%7D)
P₂=275 kPa
So the final pressure of the gas is 275 kPa.