Answer:
They will be 140 miles apart 8 hours after the first boy started the trip or 6 hours after the second boy started the trip.
Explanation:
x = the time that the first boy travels at 14 mph
x - 2 = the time the second boy travels at 14 mph
140 the distance between them
Since one travels north and the other east (their roads are perpendicular) the distance between them can be calculated using Pythagorean Theorem
(14*x)^2 + ((x-2)*14)^2 = 140^2
the solutions of the quadratic equation are
x1 = - 6 is not the solution since x > 0
x2 = 8 h is the solution
Answer:
![m=5.78\times 10^{-3}\ g](https://tex.z-dn.net/?f=m%3D5.78%5Ctimes%2010%5E%7B-3%7D%5C%20g)
is the no. of electrons
Explanation:
Given:
- quantity of charge transferred,
![Q=31\ C](https://tex.z-dn.net/?f=Q%3D31%5C%20C)
<u>No. of electrons in the given amount of charge:</u>
As we have charge on one electron ![1.602\times 10^{-19}\ C](https://tex.z-dn.net/?f=1.602%5Ctimes%2010%5E%7B-19%7D%5C%20C)
so,
![n_e=\frac{Q}{e}](https://tex.z-dn.net/?f=n_e%3D%5Cfrac%7BQ%7D%7Be%7D)
![n_e=\frac{31}{1.602\times 10^{-19}}](https://tex.z-dn.net/?f=n_e%3D%5Cfrac%7B31%7D%7B1.602%5Ctimes%2010%5E%7B-19%7D%7D)
is the no. of electrons
- Now if each water molecules donates one electron:
Then we require
molecules.
<u>Now the no. of moles in this many molecules:</u>
![n_m=\frac{n}{N_A}](https://tex.z-dn.net/?f=n_m%3D%5Cfrac%7Bn%7D%7BN_A%7D)
where
Avogadro No.
![n_m=\frac{1.935\times 10^{20}}{6.022\times 10^{23}}](https://tex.z-dn.net/?f=n_m%3D%5Cfrac%7B1.935%5Ctimes%2010%5E%7B20%7D%7D%7B6.022%5Ctimes%2010%5E%7B23%7D%7D)
![n_m=3.213\times 10^{-4}\ moles](https://tex.z-dn.net/?f=n_m%3D3.213%5Ctimes%2010%5E%7B-4%7D%5C%20moles)
- We have molecular mass of water as M=18 g/mol.
<u>So, the mass of water in the obtained moles:</u>
![n_m=\frac{m}{M}](https://tex.z-dn.net/?f=n_m%3D%5Cfrac%7Bm%7D%7BM%7D)
where:
m = mass in gram
![3.213\times 10^{-4}=\frac{m}{18}](https://tex.z-dn.net/?f=3.213%5Ctimes%2010%5E%7B-4%7D%3D%5Cfrac%7Bm%7D%7B18%7D)
![m=5.78\times 10^{-3}\ g](https://tex.z-dn.net/?f=m%3D5.78%5Ctimes%2010%5E%7B-3%7D%5C%20g)
Answer:
The final velocity of the wooden block is equal to ![1.035 m/s](https://tex.z-dn.net/?f=1.035%20m%2Fs)
Explanation:
Given that mass of bullet =
Mass of wood = ![m_{w} = 7kg](https://tex.z-dn.net/?f=m_%7Bw%7D%20%3D%207kg)
Initial velocity of bullet = ![u_{b} = 350m/s](https://tex.z-dn.net/?f=u_%7Bb%7D%20%3D%20350m%2Fs)
Final velocity of bullet = ![v_{b} = 60m/s](https://tex.z-dn.net/?f=v_%7Bb%7D%20%3D%2060m%2Fs)
Initial velocity of wood = o
Final velocity of wood = ![v_{w]](https://tex.z-dn.net/?f=v_%7Bw%5D)
Here momentum is conserved so initial momentum = final momentum
.
Upon substituting these values in above equation , we get
.