Question

An inertial frame of reference is one in which Newton's laws hold. Any frame of reference that moves at a constant speed relative to an inertial frame of reference is also an inertial frame. The proper length of an object is defined to be the length of the object as measured in the object's rest frame. If the length of the object is measured in any other inertial frame, moving with speed u relative to the object's rest frame (in a direction parallel to Lo), the resulting length is given by the length contraction equation, L space equal space L subscript o square root of 1 minus u to the power of 2 space end exponent divided by c to the power of 2 end rootwhere c is the speed of light. Similarly, if two events occur at the same spatial point in a particular reference frame, and an observer at rest in this frame measures the time interval between these two events, the time interval so measured is defined to be the proper time to. When the time interval is measured in any other inertial frame, again moving with speed u relative to the first frame, the resulting time interval t is given by the time dilation equation,Syntax error. Two spaceships, named A and B, are flying toward each other with relative speed 0.8 c. The captain of ship A fires a missile that is 2 m long at ship B. The captain of ship B measures the length of the missile as 1.25 m. What is the speed of the missile relative to ship B? Express answer as a fraction of c.

Answer 1

Considering space contraction, we know that:

`x^{^(\prime)}=x\sqrt[\placeholder{⬚}]{1-(v^2)/(c^2)}`

By replacing the values we get:

`1.25=2\sqrt[\placeholder{⬚}]{1-v_c^2}\Rightarrow((1.25)/(2))^2=1-v_c^2\Rightarrow v_c^2=1-((1.25)/(2))^2`
`v_c=\sqrt[\placeholder{⬚}]{1-((1.25)/(2))^2}\Rightarrow v_c=0.78c`

Thus, v=0.78c