Physics, 22.04.2020 02:56 jahazielBrainly15006

A cue ball of mass m1 = 0.34 kg is shot at another billiard ball, with mass m2 = 0.575 kg, which is at rest. The cue ball has an initial speed of v = 7.5 m/s in the positive direction. Assume that the collision is elastic and exactly head-on.

a) write an expression for the horizontal component of the billiard ball's velocity, vr after the collision, in terms of the other variables of the problem.
b) what is this velocity, in meters per second?
c) Write an expression for the horizontal component of the cue ball's velocity, vr, after the collision.
d) what is the horizontal component of the cue ball's final velocity, in meters per second?

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Answer from: kiki4832

Part(a): The expression for the velocity of the billiard ball is $\bf{v_{2f} = \dfrac{2m_{1}v}{m_{1}+m_{2}}}$

Part(b): The value of the velocity of the billiard ball is $\bf{5.57~m/s}$ .

Part(c): The expression for the velocity of the cue ball is $\bf{v_{1f} = \dfrac{(m_{1} - m_{2})v}{m_{1}+m_{2}}}$

Part(d): The value of the velocity of the cue ball is $\bf{1.93~m/s}$ .

Explanation:

Given:

The mass of the cue ball, $m_{1} = 0.34~kg$ .

The mass of the billiard ball, $m_{2} = 0.575~kg$ .

The initial velocity of the cue ball, $u_{1} = 7.5~m/s$

The initial velocity of the billiard ball, $u_{2} = 0$

(a)

Consider the final velocity of the cue ball be $v_{1}$ and the final velocity of the billiard ball be $v_{2}$ .

From the conservation of linear momentum , we can write

$~~~~&& m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2}\\&or,& m_{1}(u_{1} - v_{1}) = m_{2}(v_{2} - u_{2})~~~~~~~~~~~~~~~~~~~~~~(1)$

From the conservation of energy, we can write

$~~~&& \dfrac{1}{2}m_{1}u_{1}^{2} + \dfrac{1}{2}m_{2}u_{2}^{2} = \dfrac{1}{2}m_{1}v_{1}^{2} + \dfrac{1}{2}m_{2}v_{2}^{2}\\&or,& \dfrac{1}{2}m_{1}(u_{1}^{2} - v_{1}^{2}) = \dfrac{1}{2}m_{2}(v_{2}^{2} - u_{2}^{2})~~~~~~~~~~~~~~~~~~~~~~~(2)$

Dividing equation (1) by equation (2), we have

$~~~&& \dfrac{m_{1}(u_{1} - v_{1}) }{m_{1}(u_{1}^{2} - v_{1}^{2})} = \dfrac{m_{2}(v_{2} - u_{2})}{m_{2}(v_{2}^{2} - u_{2}^{2})}\\&or,& u_{1} + v_{1} = u_{2} + v_{2}~~~~~~~~~~~~~~~~~~~~~~~~(3)$

Rearranging equation (3) for $v_{1}$ , we have

$v_{1} = u_{2} + v_{2} - u_{1}~~~~~~~~~~~~~~~~~~~~(4)$

Substitute equation (4) in equation (1), we can write

$v_{2} = \dfrac{2m_{1}u_{1}}{m_{1}+m_{2}} + \dfrac{m_{2} - m_{1}}{m_{1} + m_{2}}u_{2}~~~~~~~~~~~~~~(5)$

Substituting for $u_{2}$ , for $u_{1}$ and $v_{2f}$ for $v_{2}$ in equation (5), we have

$v_{2f} = \dfrac{2m_{1}v}{m_{1}+m_{2}}~~~~~~~~~~~~~~~~~~~~~~~~(6)$

(b)

Substituting 0.34~kg for $m_{1}$ , 7.5~m/s for and 0.575~kg for $m_{2}$ in equation (6), we have

$v_{2f} &=& \dfrac{2(0.34~kg)(7.5~m/s)}{(0.34 + 0.575)~kg}\\~~~~~&=& 5.57~m/s$

(c)

Rearranging equation(3) for $v_{2}$ , we have

$v_{2} = u_{1} + v_{1} – u_{2}~~~~~~~~~~~~~~~~~~~~(7)$

Substitute equation (7) in equation (1), we can write

$v_{1} = \dfrac{2m_{2}u_{2}}{m_{1}+m_{2}} + \dfrac{m_{1} - m_{2}}{m_{1} + m_{2}}u_{2}~~~~~~~~~~~~~~(8)$

Substituting for $u_{2}$ , for $u_{1}$ and $v_{1f}$ for $v_{1}$ in equation (8), we have

$v_{1f} = \dfrac{(m_{1} - m_{2})v}{m_{1}+m_{2}}~~~~~~~~~~~~~~~~~~~~~~~~(9)$

(d)

Substituting 0.34~kg for $m_{1}$ , 7.5~m/s for and 0.575~kg for $m_{2}$ in equation (9), we have

$v_{1f} &=& \dfrac{(0.34 - 0.575)~kg(7.5~m/s)}{(0.34 + 0.575)~kg}\\~~~~~&=& -1.93~m/s$

Negative sign indicates that the cue ball will bounce back.

Answer from: Quest

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account. she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem. she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem. her desire for the new hairstyle is in conflict with her honesty and integrity.

d. if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it. the amount she has in her account is not the problem. and if i may suggest, she might as well close her checking account, and put the money where it'll work for her. it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now. under no circumstances should he ask for a higher limit.

b. he can ask for the grace period to be extended. but that's no solution, the bank will almost certainly refuse anyway, and there are much better options. he knew the rules of his credit card when he started using it.

c. he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d. he definitely should pay the minimum otherwise they could shut down his card. he should also pay as much more as he possibly can. he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices. what he has to do: pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.

Answer from: Quest

It is d, all the other ones say incorrect answer .

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A cue ball of mass m1 = 0.34 kg is shot at another billiard ball, with mass m2 = 0.575 kg, which is...

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