derive the formula for relative velocity
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Hello buddy..
Check out this..
t′=γ(t−Vxc2)t′=γ(t−Vxc2)
x′=γ(x−Vt)x′=γ(x−Vt)
Take the differential,
dt′=γ(dt−Vdxc2)dt′=γ(dt−Vdxc2)
dx′=γ(dx−Vdt)dx′=γ(dx−Vdt)
Now, the velocity of an object is v=dx/dt in the rest frame, but in the frame boosted with velocity V, it is dx'/dt', which is then
dx′dt′=dx−Vdtdt−Vdx/c2=v−V1−vV/c2dx′dt′=dx−Vdtdt−Vdx/c2=v−V1−vV/c2
Suppose in the rest frame you have 2 objects, one moving with speed V1V1 and the other moving with speed V2V2. To find the relative velocity in the frame of object 1, you should perform a boost to the frame moving with velocity V1V1. In this case, the v=V2v=V2 and V=V1V=V1 in the formula above.
Hope it helps you buddy
Check out this..
t′=γ(t−Vxc2)t′=γ(t−Vxc2)
x′=γ(x−Vt)x′=γ(x−Vt)
Take the differential,
dt′=γ(dt−Vdxc2)dt′=γ(dt−Vdxc2)
dx′=γ(dx−Vdt)dx′=γ(dx−Vdt)
Now, the velocity of an object is v=dx/dt in the rest frame, but in the frame boosted with velocity V, it is dx'/dt', which is then
dx′dt′=dx−Vdtdt−Vdx/c2=v−V1−vV/c2dx′dt′=dx−Vdtdt−Vdx/c2=v−V1−vV/c2
Suppose in the rest frame you have 2 objects, one moving with speed V1V1 and the other moving with speed V2V2. To find the relative velocity in the frame of object 1, you should perform a boost to the frame moving with velocity V1V1. In this case, the v=V2v=V2 and V=V1V=V1 in the formula above.
Hope it helps you buddy
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