The compass is designed and developed to use a pendulous system to improve horizontality.
<h3>What is a compass?</h3>
A compass can be defined as a scientific instrument that contains a magnetized pointer, which is used to show and indicate the following four (4) main cardinal directions:
Basically, the compass is a scientific instrument that's designed and developed to use a pendulous system to improve horizontality.
Read more on compass here: brainly.com/question/11165627
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Answer:
a) t = 3.35[s]; b) t = 1.386[s]
Explanation:
We can solve this problem by dividing it into two parts, for the first 55 [m] and then the second part with the remaining 55 [m].
We will take the initial velocity as zero, as the problem does not mention that the Rock was thrown at initial velocity.
And using kinematics equations:
![v_{f}^{2}= v_{o}^{2}+2*g*y\\where:\\v_{o}=0\\g=gravity = 9.81[m/s^2]\\y=55 [m]\\v_{f}^{2}=0+2*9.81*55\\v_{f}=\sqrt{2*9.81*55} \\v_{f}=32.85[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%3D%20v_%7Bo%7D%5E%7B2%7D%2B2%2Ag%2Ay%5C%5Cwhere%3A%5C%5Cv_%7Bo%7D%3D0%5C%5Cg%3Dgravity%20%3D%209.81%5Bm%2Fs%5E2%5D%5C%5Cy%3D55%20%5Bm%5D%5C%5Cv_%7Bf%7D%5E%7B2%7D%3D0%2B2%2A9.81%2A55%5C%5Cv_%7Bf%7D%3D%5Csqrt%7B2%2A9.81%2A55%7D%20%5C%5Cv_%7Bf%7D%3D32.85%5Bm%2Fs%5D)
Now we can calculate the time:
![v_{f}=v_{o}+g*t\\t=\frac{v_{f}-v_{o}}{g}\\ t=\frac{32.85-0}{9.81}\\ t=3.35[s]](https://tex.z-dn.net/?f=v_%7Bf%7D%3Dv_%7Bo%7D%2Bg%2At%5C%5Ct%3D%5Cfrac%7Bv_%7Bf%7D-v_%7Bo%7D%7D%7Bg%7D%5C%5C%20t%3D%5Cfrac%7B32.85-0%7D%7B9.81%7D%5C%5C%20t%3D3.35%5Bs%5D)
Now we can calculate the second time, but using as a initial velocity 32.85[m/s].
The final velocity will be:
![v_{f}^{2}= v_{o}^{2}+2*g*y\\v_{f}=\sqrt{v_{o}^{2}+2*g*y} \\v_{f}=\sqrt{32.85^{2}+2*9.81*55 } \\v_{f}=46.45[m/s]](https://tex.z-dn.net/?f=v_%7Bf%7D%5E%7B2%7D%3D%20v_%7Bo%7D%5E%7B2%7D%2B2%2Ag%2Ay%5C%5Cv_%7Bf%7D%3D%5Csqrt%7Bv_%7Bo%7D%5E%7B2%7D%2B2%2Ag%2Ay%7D%20%5C%5Cv_%7Bf%7D%3D%5Csqrt%7B32.85%5E%7B2%7D%2B2%2A9.81%2A55%20%7D%20%5C%5Cv_%7Bf%7D%3D46.45%5Bm%2Fs%5D)
Now we can calculate the second time:
![t=\frac{46.45-32.85}{9.81} \\t= 1.386[s]](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B46.45-32.85%7D%7B9.81%7D%20%5C%5Ct%3D%201.386%5Bs%5D)
Note: The reason the second time is shorter even though it is the same distance is that the acceleration of gravity increases the speed of the rock more and more as it falls.
According to Charles law, we know, at constant pressure, volume is directly proportional to temperature.
So, <span>V/T = constant
</span>
V₁/t₁ = V₂/t₂
V₁t₂ = V₂t₁
Here, we have: V₁ = 9 mL
V₂ = ?
T₂ = 50+272 = 323 K
T₁ = 19+273 = 292 K
Substitute their values into the expression:
9 × 323 = V₂ × 292
V₂ = 2907 / 292
V₂ = 9.95
After rounding-off to unit place value, it would be equal to 10 mL
So, In short Option C would be your correct answer.
Hope this helps!
