Answer:
Given that
![\overrightarrow{v_{a}}=3\widehat{i}\\\\\overrightarrow{v_{b}}=4\widehat{i}+\widehat{j}\\\\\therefore \overrightarrow{v_{ba}}=4\widehat{i}+\widehat{j}-3\widehat{i}\\\\\overrightarrow{v_{ba}}=\widehat{i}+\widehat{j}\\\\\frac{\overrightarrow{dr_{ba}}}{dt}=\widehat{i}+\widehat{j}\\\\\therefore \overrightarrow{r_{ba}}=\int (\widehat{i}+\widehat{j})dt\\\\\therefore \overrightarrow{r_{ba}}=t\widehat{i}+t\widehat{j}+\overrightarrow{r_{o}}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Bv_%7Ba%7D%7D%3D3%5Cwidehat%7Bi%7D%5C%5C%5C%5C%5Coverrightarrow%7Bv_%7Bb%7D%7D%3D4%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%5C%5C%5C%5C%5Ctherefore%20%5Coverrightarrow%7Bv_%7Bba%7D%7D%3D4%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D-3%5Cwidehat%7Bi%7D%5C%5C%5C%5C%5Coverrightarrow%7Bv_%7Bba%7D%7D%3D%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%5C%5C%5C%5C%5Cfrac%7B%5Coverrightarrow%7Bdr_%7Bba%7D%7D%7D%7Bdt%7D%3D%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%5C%5C%5C%5C%5Ctherefore%20%5Coverrightarrow%7Br_%7Bba%7D%7D%3D%5Cint%20%28%5Cwidehat%7Bi%7D%2B%5Cwidehat%7Bj%7D%29dt%5C%5C%5C%5C%5Ctherefore%20%5Coverrightarrow%7Br_%7Bba%7D%7D%3Dt%5Cwidehat%7Bi%7D%2Bt%5Cwidehat%7Bj%7D%2B%5Coverrightarrow%7Br_%7Bo%7D%7D)
Now it is given that
![\overrightarrow{r_{o}}=-2\widehat{i}-6\widehat{j}](https://tex.z-dn.net/?f=%5Coverrightarrow%7Br_%7Bo%7D%7D%3D-2%5Cwidehat%7Bi%7D-6%5Cwidehat%7Bj%7D)
![\therefore \overrightarrow{r_{ba}}=(t-2)\widehat{i}+(t-6)\widehat{j}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Coverrightarrow%7Br_%7Bba%7D%7D%3D%28t-2%29%5Cwidehat%7Bi%7D%2B%28t-6%29%5Cwidehat%7Bj%7D)
Now the distance can be calculates as
![r=\sqrt{x^{2}+y^{2}}\\\\r^{2}=(t-2)^{2}+(t-6)^{2}\\\\](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D%5C%5C%5C%5Cr%5E%7B2%7D%3D%28t-2%29%5E%7B2%7D%2B%28t-6%29%5E%7B2%7D%5C%5C%5C%5C)
Differentiating with respect to 't' and equating to zero for minimizing the function we get
![r=\sqrt{x^{2}+y^{2}}\\\\r^{2}=(t-2)^{2}+(t-6)^{2}\\\\2r\frac{dr}{dt}=2(t-2)+2(t-6)\\\\2r\frac{dr}{dt}=4t-16\\\\\therefore \frac{dr}{dt}=0\\\\\Rightarrow 4t-16=0\\\\\therefore t=4](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E%7B2%7D%2By%5E%7B2%7D%7D%5C%5C%5C%5Cr%5E%7B2%7D%3D%28t-2%29%5E%7B2%7D%2B%28t-6%29%5E%7B2%7D%5C%5C%5C%5C2r%5Cfrac%7Bdr%7D%7Bdt%7D%3D2%28t-2%29%2B2%28t-6%29%5C%5C%5C%5C2r%5Cfrac%7Bdr%7D%7Bdt%7D%3D4t-16%5C%5C%5C%5C%5Ctherefore%20%5Cfrac%7Bdr%7D%7Bdt%7D%3D0%5C%5C%5C%5C%5CRightarrow%204t-16%3D0%5C%5C%5C%5C%5Ctherefore%20t%3D4)
The shortest distance is thus given by
![r^{2}=(4-2)^{2}+(4-6)^{2}\\\\r=2\sqrt{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D%3D%284-2%29%5E%7B2%7D%2B%284-6%29%5E%7B2%7D%5C%5C%5C%5Cr%3D2%5Csqrt%7B2%7D)
Answer:
FG and FP
Explanation:
Gravitational Force(FG) because the box is being pulled down and a resistance force pushing up because he is pushing(FP) up on the box.
I hope this helps!
The value of 3993 BTUs in Joules is 4212838.0195 Joules.
Answer:
thats a good question
Explanation:
i might need help for this.