Time dilation: a missile moves with speed 6.5-10 m/s with respect to an observer on the ground. how long will it take the missile's clock to fall behind the ground observer's clock by 1 millisecond? hint: use the binomial formula: (1+x)a1+ ax.

The time taken by missile's clock is

Solution:

As per the question:

Speed of the missile,

Now,

If 'T' be the time of the frame at rest then the dilated time as per the question is given as:

T' = T + 1

Now, using the time dilation eqn:

        (1)

Using binomial theorem in the above eqn:

We know that:

Thus eqn (1) becomes:

Now, putting appropriate values in the above eqn:

grav force prop 1/r squared 2r all squared is 4rsquared 1/4rsquared quartered