Velocity Addition: Solving the Mystery

[Mivz18]

I'm trying to figure this problem out, and think it's not that hard, but am having trouble acquiring the answer. Here is the problem:

You and a friend decide to "hitch" a ride in the mailcar of a train heading to Green Bay (due north). Halfway there, your friend asks you for a sandwich out of your backpack. As you throw the sandwich to him, it travels at a speed of 0.20c relative to himself and due north. If the train is moving at 0.50c and a cop sitting stationary at the railroad tracks observes your throw, what speed would he clock the sandwich at if he pointed his speed gun at it?

So, I use the equation for relative velocity in relativity:

v = (u+w)(1 + uw/c^2)

From this equation, I simply plug in the numbers, u = 0.50c and w = 0.20c, then I obtain 2.31E8 m/s . However, this seems kind of strange since the velocity observed by the cop should be less than .7c and 2.31E8 is greater than .7c . Am I doing something wrong?

 

[Physics_wiz]

wouldn't the answer be just .7c? I'm not an expert in this and I haven't studied relativity yet (soon tho) but my understanding is that you just add the speeds in all frames of reference except when dealing with light.

 

[Physics_wiz]

However, this seems kind of strange since the velocity observed by the cop should be less than .7c and 2.31E8 is greater than .7c . Am I doing something wrong?

With the equation you give, the speed has to be greater than .7c because you are multiplying (u+w) by a number bigger than 1 and (u+w)=.7c (as long as u and w are positive).

 

[Mivz18]

No, it can't because in theory, nothing is faster than the speed of light. Therefore, if we consider the vector addition of regular (slower) speeds as learned in beginning physics, you will run into a problem which I was shown in the help. As you increase the speed of the sandwich to 0.5c and 0.6c, the speed the cop would clock the sandwich at would be greater than or equal to the speed of light, which is considered to be impossible. So I don't know if I've calculated this problem correctly. I have the right equation. However, am I plugging in the data correctly. What really stumps me is that the variable it asks for is u, when I thought we were looking for v . So I'm lost. Help?!?

 

[Physics_wiz]

.7c is not greater than the speed of light. If the sandwich was moving at .8c then you'd have a problem but right now u+w = .7c which is less than c.

But like I said, I'm no expert on this. Sorry if I'm not helping

 

[Mivz18]

https://tycho-s.physics.wisc.edu/cgi/courses/shell/phys170/fall04/ie.pl?08/velocity

This is the link to the online problem I'm doing. Try the help and you'll see what I'm talking about. Maybe that may help you help me, lol.

 

[Physics_wiz]

"Enter your NetID: "

 

[Physics_wiz]

Sorry Mivz18, but I have to go sleep now (not like I was any help). Good luck with the problem.

 

[Mivz18]

Nevermind, I found my mistake. I was supposed to divide the second quantity by the first, not multiply, an error by the help. Thanks for your help though Physics_wiz!