Answer:
t = 2.2 s
Explanation:
Given that,
Height of the roof, h = 24.15 m
The initial velocity of the pumpkin, u = 0
We need to find the time taken for the pumpkin to hit the ground. Let the time be t. Using second equation of kinematics to find it as follows :

Here, u = 0 and a = g

So, it will take 2.22 s for the pumpkin to hit the ground.
R is proportional to the length of the wire:
R ∝ length
R is also proportional to the inverse square of the diameter:
R ∝ 1/diameter²
The resistance of a wire 2700ft long with a diameter of 0.26in is 9850Ω. Now let's change the shape of the wire, adding and subtracting material as we go along, such that the wire is now 2800ft and has a diameter of 0.1in.
Calculate the scale factor due to the changed length:
k₁ = 2800/2700 = 1.037
Scale factor due to changed diameter:
k₂ = 1/(0.1/0.26)² = 6.76
Multiply the original resistance by these factors to get the new resistance:
R = R₀k₁k₂
R₀ = 9850Ω, k₁ = 1.037, k₂ = 6.76
R = 9850(1.037)(6.76)
R = 69049.682Ω
Round to the nearest hundredth:
R = 69049.68Ω
Answer:
The explosive force experienced by the shell inside the barrel is 23437500 newtons.
Explanation:
Let suppose that shells are not experiencing any effect from non-conservative forces (i.e. friction, air viscosity) and changes in gravitational potential energy are negligible. The explosive force experienced by the shell inside the barrel can be estimated by Work-Energy Theorem, represented by the following formula:
(1)
Where:
- Explosive force, measured in newtons.
- Barrel length, measured in meters.
- Mass of the shell, measured in kilograms.
,
- Initial and final speeds of the shell, measured in meters per second.
If we know that
,
,
and
, then the explosive force experienced by the shell inside the barrel is:

![F = \frac{(1250\,kg)\cdot \left[\left(750\,\frac{m}{s} \right)^{2}-\left(0\,\frac{m}{s} \right)^{2}\right]}{2\cdot (15\,m)}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%7B%281250%5C%2Ckg%29%5Ccdot%20%5Cleft%5B%5Cleft%28750%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D-%5Cleft%280%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%5Cright%29%5E%7B2%7D%5Cright%5D%7D%7B2%5Ccdot%20%2815%5C%2Cm%29%7D)

The explosive force experienced by the shell inside the barrel is 23437500 newtons.
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