Ive been trying the last part (part C) of this question for ages now and can't see what Im doing wrong: https://isaacphysics.org/questions/manipulation_5_5?board=c320ab30-d117-4fbd-b5e4-167e1fef400e&stage=a_level

The answer to part B is (X + v*T) * gamma == x. Now part C wants t in terms of X T v c and gamma, so Ive just been rearranging the equation for T in part B and substituting in the answer for X in terms of the other constants. I don't see anything wrong with that, it's all in terms of the correct constants, but Isaac Physics doesn't seem to like it. Ive tried using the equation for X, Ive tried substituting gamma as 1/sqrt(1-v^2/c^2) Ive tried simplifying the fraction. Im convinced Ive tried everything so if anyone could help that would be great, maybe there is a problem with my method.

The answer to part B is (X + v*T) * gamma == x. Now part C wants t in terms of X T v c and gamma, so Ive just been rearranging the equation for T in part B and substituting in the answer for X in terms of the other constants. I don't see anything wrong with that, it's all in terms of the correct constants, but Isaac Physics doesn't seem to like it. Ive tried using the equation for X, Ive tried substituting gamma as 1/sqrt(1-v^2/c^2) Ive tried simplifying the fraction. Im convinced Ive tried everything so if anyone could help that would be great, maybe there is a problem with my method.

Original post by Yhghnb

Ive been trying the last part (part C) of this question for ages now and can't see what Im doing wrong: https://isaacphysics.org/questions/manipulation_5_5?board=c320ab30-d117-4fbd-b5e4-167e1fef400e&stage=a_level

The answer to part B is (X + v*T) * gamma == x. Now part C wants t in terms of X T v c and gamma, so Ive just been rearranging the equation for T in part B and substituting in the answer for X in terms of the other constants. I don't see anything wrong with that, it's all in terms of the correct constants, but Isaac Physics doesn't seem to like it. Ive tried using the equation for X, Ive tried substituting gamma as 1/sqrt(1-v^2/c^2) Ive tried simplifying the fraction. Im convinced Ive tried everything so if anyone could help that would be great, maybe there is a problem with my method.

The answer to part B is (X + v*T) * gamma == x. Now part C wants t in terms of X T v c and gamma, so Ive just been rearranging the equation for T in part B and substituting in the answer for X in terms of the other constants. I don't see anything wrong with that, it's all in terms of the correct constants, but Isaac Physics doesn't seem to like it. Ive tried using the equation for X, Ive tried substituting gamma as 1/sqrt(1-v^2/c^2) Ive tried simplifying the fraction. Im convinced Ive tried everything so if anyone could help that would be great, maybe there is a problem with my method.

Original post by Yhghnb

Ive rearranged equation T= gamma(t-vx/c^2) for t: t=T/gamma + vx/c^2 then substituted in x and have T/gamma + v(X+vT)gamma/c^2. This is in all the correct constants but it incorrect according to Isaac physics.

looks like youve done the sub for x incorrectly.

(edited 3 months ago)

Original post by mqb2766

looks like youve done the sub for x incorrectly.

accidentally sent my response twice. How have I substituted x incorrectly? Im not sure if im just being ridiculously stupid or not, but I have x = (X + vT) gamma so If I pop that in where x is it should be correct, right?

Original post by Yhghnb

accidentally sent my response twice. How have I substituted x incorrectly? Im not sure if im just being ridiculously stupid or not, but I have x = (X + vT) gamma so If I pop that in where x is it should be correct, right?

From the first equation you have

x = X/gamma + vt

Then sub that in.

Original post by mqb2766

From the first equation you have

x = X/gamma + vt

Then sub that in.

x = X/gamma + vt

Then sub that in.

Not sure if this is a problem with my rearranging skills, but if I do that then substitute it into equation two I get T/gamma+ (v (X/gamma +vt))/c^2=t Which is still wrong. Let me know if I just can't do maths because thats highly likely as well.

Original post by Yhghnb

Not sure if this is a problem with my rearranging skills, but if I do that then substitute it into equation two I get T/gamma+ (v (X/gamma +vt))/c^2=t Which is still wrong. Let me know if I just can't do maths because thats highly likely as well.

Youve got to put both terms involving t on the same side, then factorise t and divide by term that multiplies it.

Original post by mqb2766

Youve got to put both terms involving t on the same side, then factorise t and divide by term that multiplies it.

oh wow yeah, im not being particularly clever today. Once you get to (Tc^2+ vX)/gamma = t(c^2 -v^2) and divide by (c^2-v^2) its still saying Im wrong. Ive got this written down in the equation editor: ((Tc^2+vX)/(gamma))/(c^2-v^2)=t. Am I being thick again?

Original post by Yhghnb

oh wow yeah, im not being particularly clever today. Once you get to (Tc^2+ vX)/gamma = t(c^2 -v^2) and divide by (c^2-v^2) its still saying Im wrong. Ive got this written down in the equation editor: ((Tc^2+vX)/(gamma))/(c^2-v^2)=t. Am I being thick again?

Original post by mqb2766

Not far off. When you factorised t you should have noticed that the other term was ... which means you can cancel a bit. Dont multiply through by c^2.

Ive just tried again and come up with t= (Tc^2 +vX)/(gamma (c^2 -v^2)) There was one bit that cancelled like you said. But still wrong. Not sure why I can't seem to rearrange today, but any more help would be appreciated.

Original post by Yhghnb

Ive just tried again and come up with t= (Tc^2 +vX)/(gamma (c^2 -v^2)) There was one bit that cancelled like you said. But still wrong. Not sure why I can't seem to rearrange today, but any more help would be appreciated.

Dont multiply through by c^2, so you have

t(1 - v^2/c^2) = (T + vX/c^2) / gamma

As in the previous post, think about what multiplies t, sub and cancel.

Original post by mqb2766

Dont multiply through by c^2, so you have

t(1 - v^2/c^2) = (T + vX/c^2) / gamma

As in the previous post, think about what multiplies t, sub and cancel.

t(1 - v^2/c^2) = (T + vX/c^2) / gamma

As in the previous post, think about what multiplies t, sub and cancel.

Ok thanks very much just got it. Not sure why that took me so long, maybe I just kept on getting confused with all the Ts and stuff. Thanks again.

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