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1. The problem statement, all variables and given/known data
Mary and Frank are each in their own rocket ships moving along the xaxis. Mary's ship passes Frank's ship at t_{0}=t_{0}'=0 with a speed "v" to the right. When t=t_{1} in Frank's frame, Frank shoots a missile with a speed "u" where u>v in the direction of Mary. At time t=t_{2} in Frank's frame the missile hits Mary's ship.
a. Show the process of events on an xt diagram showing Frank, Mary, and the missiles position as a function of time.
Given [t_{1}, u, v ] Determine,
b. The slope and y intercept of Mary's motion on the diagram
c. The slope and y intercept of the missile on the diagram
d. From the two lines, calculate the time t_{2} and the positions x_{1} and x_{2} of the missile in Frank's frame
e. Using Galilean transformations, determine the time t_{1}' and t_{2}' of the events in Mary's frame.
f. Using Galilean transformations, determine the positions x_{1}' and x_{2}' of the missile in Mary's frame.
*Everything here is written exactly as it is on the sheet. Didn't change a thing.
2. Relevant equations
t=t'
x'=xvt
y'=y
x=x_{0}+v_{0}t+1/2at^{2}
v=v_{0}+at
u_{x}'=u_{x}v
u_{y}'=u_{y}
3. The attempt at a solution
This problem has me very confused and I am not sure if the wording is off or if I'm simply not understanding.
Mary passes Frank with a speed of v relative to what?
In Frank's frame he fires a missile at speed u which is apparently greater than v but to Frank, Mary wouldn't be travelling at v right? She'd be travelling at v minus Frank's speed.
Ignore what I believe to be an inconsistency, I drew this picture of their positions with respect to time from an observer's frame.
and this one from Frank's frame
to b) and c) I wrote that Mary's slope is v and the missiles slope is u, while both their yintercepts are 0 because they're both moving along the xaxis. (I'm unsure if by yintercepts it actually means tintercepts)
but I get stuck on d), e), and f) using either method
edit
for d) I did the following
From Frank's frame
x_{1} = 0 for the missile.
u(t_{2}t_{1}) = vt_{2}
isolating for t_{2} gets t_{2} = ((ut_{1})/(uv))
and
x_{2} = ((u^{2}t_{1})/(uv))  t_{1}
for e) I used the formula above simply saying t_{1}'=t_{1} and t_{2} = t_{2}
and f) got me
x'=xvt
x_{1}' = x_{1} vt_{1}. x_{1} = 0
x_{1}' = vt_{1}.
x_{2}'=x_{2}vt_{2}
x_{2}' = ((u^{2}t_{1})/(uv))  t_{1}  v((ut_{1})/(uv))
I feel like its totally wrong
Mary and Frank are each in their own rocket ships moving along the xaxis. Mary's ship passes Frank's ship at t_{0}=t_{0}'=0 with a speed "v" to the right. When t=t_{1} in Frank's frame, Frank shoots a missile with a speed "u" where u>v in the direction of Mary. At time t=t_{2} in Frank's frame the missile hits Mary's ship.
a. Show the process of events on an xt diagram showing Frank, Mary, and the missiles position as a function of time.
Given [t_{1}, u, v ] Determine,
b. The slope and y intercept of Mary's motion on the diagram
c. The slope and y intercept of the missile on the diagram
d. From the two lines, calculate the time t_{2} and the positions x_{1} and x_{2} of the missile in Frank's frame
e. Using Galilean transformations, determine the time t_{1}' and t_{2}' of the events in Mary's frame.
f. Using Galilean transformations, determine the positions x_{1}' and x_{2}' of the missile in Mary's frame.
*Everything here is written exactly as it is on the sheet. Didn't change a thing.
2. Relevant equations
t=t'
x'=xvt
y'=y
x=x_{0}+v_{0}t+1/2at^{2}
v=v_{0}+at
u_{x}'=u_{x}v
u_{y}'=u_{y}
3. The attempt at a solution
This problem has me very confused and I am not sure if the wording is off or if I'm simply not understanding.
Mary passes Frank with a speed of v relative to what?
In Frank's frame he fires a missile at speed u which is apparently greater than v but to Frank, Mary wouldn't be travelling at v right? She'd be travelling at v minus Frank's speed.
Ignore what I believe to be an inconsistency, I drew this picture of their positions with respect to time from an observer's frame.
and this one from Frank's frame
to b) and c) I wrote that Mary's slope is v and the missiles slope is u, while both their yintercepts are 0 because they're both moving along the xaxis. (I'm unsure if by yintercepts it actually means tintercepts)
but I get stuck on d), e), and f) using either method
edit
for d) I did the following
From Frank's frame
x_{1} = 0 for the missile.
u(t_{2}t_{1}) = vt_{2}
isolating for t_{2} gets t_{2} = ((ut_{1})/(uv))
and
x_{2} = ((u^{2}t_{1})/(uv))  t_{1}
for e) I used the formula above simply saying t_{1}'=t_{1} and t_{2} = t_{2}
and f) got me
x'=xvt
x_{1}' = x_{1} vt_{1}. x_{1} = 0
x_{1}' = vt_{1}.
x_{2}'=x_{2}vt_{2}
x_{2}' = ((u^{2}t_{1})/(uv))  t_{1}  v((ut_{1})/(uv))
I feel like its totally wrong
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