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:

this is an example of "committed" time.

committed time, as contracted time, takes need over essential and available time since it is seen as profitable work. it alludes to the time allotted to keep up a home and family. at the point when a man is commuting using committed time this individual may feel that the drive is an obligation to family, for example, strolling youngsters to class or driving a mate to work. contracted and committed time clients may feel that their commute could really compare to the commute of important or leisure time clients on the grounds that their commute is profitable work. in this manner, they might be more disposed to pick a mechanized method of movement.