I would say Option B) because Option C) is wrong since matter cannot be created. A closed system does not exchange matter so it's not Option D). Since an island is an isolated area, Option A) is wrong.
Answer:
A) the maximum acceleration the boulder can have and still get out of the quarry
B) how long does it take to be lifted out at maximum acceleration if it started from rest
Explanation:
A)
let +y is upward. look below at the free body diagram. the mass M refers to the combined mass of the boulder and chain.
the weight of the chain is:
and maximum tension is ![T=2.50 m_{c} g=1.41*10^4N](https://tex.z-dn.net/?f=T%3D2.50%20m_%7Bc%7D%20g%3D1.41%2A10%5E4N)
total mass and weight is :
![M =m_{c}+ m_{b} =740kg+550kg=1290 kg](https://tex.z-dn.net/?f=M%20%3Dm_%7Bc%7D%2B%20m_%7Bb%7D%20%3D740kg%2B550kg%3D1290%20kg)
![w_{M} =1.2650*10^4N](https://tex.z-dn.net/?f=w_%7BM%7D%20%3D1.2650%2A10%5E4N)
∑![F_{y} =ma_{y}](https://tex.z-dn.net/?f=F_%7By%7D%20%3Dma_%7By%7D)
![T-M_{g} =Ma_{y}](https://tex.z-dn.net/?f=T-M_%7Bg%7D%20%3DMa_%7By%7D)
![a_{y} =(t-M_{g} )/M=(2.50m_{c} -M_{g} )/M=(2.50.550kg-1290kg)(9.8m/s^2)/1290kg](https://tex.z-dn.net/?f=a_%7By%7D%20%3D%28t-M_%7Bg%7D%20%29%2FM%3D%282.50m_%7Bc%7D%20-M_%7Bg%7D%20%29%2FM%3D%282.50.550kg-1290kg%29%289.8m%2Fs%5E2%29%2F1290kg)
![=0.645m/s^2](https://tex.z-dn.net/?f=%3D0.645m%2Fs%5E2)
B)
maximum acceleration
![a_{y} =0.645m/s^2\\\\y-y_{0} =119m\\v_{0y} =0](https://tex.z-dn.net/?f=a_%7By%7D%20%3D0.645m%2Fs%5E2%5C%5C%5C%5Cy-y_%7B0%7D%20%3D119m%5C%5Cv_%7B0y%7D%20%3D0)
using ![y-y_{0} =v_{oy} t+1/2(a_{y} )t^2](https://tex.z-dn.net/?f=y-y_%7B0%7D%20%3Dv_%7Boy%7D%20t%2B1%2F2%28a_%7By%7D%20%29t%5E2)
to solve for t
![t=\sqrt{2(y-y_{0} )/a_{y} }](https://tex.z-dn.net/?f=t%3D%5Csqrt%7B2%28y-y_%7B0%7D%20%29%2Fa_%7By%7D%20%7D)
![t=\sqrt{2(119m)/0.645m/s^2} =19.20s](https://tex.z-dn.net/?f=t%3D%5Csqrt%7B2%28119m%29%2F0.645m%2Fs%5E2%7D%20%3D19.20s)
I found the answer for you if u need any help ask anytime!
Answer:
![\theta = 211.7 degree](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20211.7%20degree)
Explanation:
First displacement of the particle is given as
= 11 m at 82 degree with positive X axis
so we can say
![\vec r_1 = 11 cos82 \hat i + 11 sin82 \hat j](https://tex.z-dn.net/?f=%5Cvec%20r_1%20%3D%2011%20cos82%20%5Chat%20i%20%2B%2011%20sin82%20%5Chat%20j)
![\vec r_1 = 1.53\hat i + 10.9 \hat j](https://tex.z-dn.net/?f=%5Cvec%20r_1%20%3D%201.53%5Chat%20i%20%2B%2010.9%20%5Chat%20j)
resultant displacement of the particle after second displacement is given as
r = 8.7 m at 135 degree with positive X axis
so we can say
![r = 8.7 cos135\hat i + 8.7 sin135\hat j](https://tex.z-dn.net/?f=r%20%3D%208.7%20cos135%5Chat%20i%20%2B%208.7%20sin135%5Chat%20j)
![r = -6.15 \hat i + 6.15 \hat j](https://tex.z-dn.net/?f=r%20%3D%20-6.15%20%5Chat%20i%20%2B%206.15%20%5Chat%20j)
now we know that
![r = r_1 + r_2](https://tex.z-dn.net/?f=r%20%3D%20r_1%20%2B%20r_2)
now we have
![r_2 = r - r_1](https://tex.z-dn.net/?f=r_2%20%3D%20r%20-%20r_1)
so we will have
![r_2 = (-6.15 \hat i + 6.15 \hat j) - (1.53\hat i + 10.9 \hat j)](https://tex.z-dn.net/?f=r_2%20%3D%20%28-6.15%20%5Chat%20i%20%2B%206.15%20%5Chat%20j%29%20-%20%281.53%5Chat%20i%20%2B%2010.9%20%5Chat%20j%29)
![r_2 = -7.68 \hat i - 4.75 \hat j](https://tex.z-dn.net/?f=r_2%20%3D%20-7.68%20%5Chat%20i%20-%204.75%20%5Chat%20j)
so angle of the second displacement is given as
![tan\theta = \frac{r_y}{r_x}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7Br_y%7D%7Br_x%7D)
![tan\theta = \frac{-4.75}{-7.68}](https://tex.z-dn.net/?f=tan%5Ctheta%20%3D%20%5Cfrac%7B-4.75%7D%7B-7.68%7D)
![\theta = 211.7 degree](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20211.7%20degree)