Answer:
a) Bullet will hit
b) Bullets will not hit
Explanation:
Given:
The velocity of the bullet, u =
in the rest frame of the bullet pursuit car
The velocity of the original frame of reference, v =
with respect to the pursuit car.
Now, according to the Galileo
the velocity of the bullet in the original frame of reference (u') will be
u' = u - v
on substituting the values we get
u' = ![\frac{1}{3}c-(-\frac{1}{2}c)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dc-%28-%5Cfrac%7B1%7D%7B2%7Dc%29)
or
u' = ![\frac{1}{3}c+\frac{1}{2}c](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dc%2B%5Cfrac%7B1%7D%7B2%7Dc)
or
u' = ![\frac{5}{6}c](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B6%7Dc)
since this velocity (
) is greater than the (
)
hence,
<u>the bullet will hit</u>
Now, according to the Einstein theory
the velocity of the bullet in the original frame of reference (u') will be
![u'=\frac{u-v}{1-\frac{uv}{c^2}}](https://tex.z-dn.net/?f=u%27%3D%5Cfrac%7Bu-v%7D%7B1-%5Cfrac%7Buv%7D%7Bc%5E2%7D%7D)
on substituting the values we get
![u'=\frac{\frac{1}{3}c-\frac{1}{2}c}{1-\frac{\frac{1}{3}c\times \frac{1}{2}c}{c^2}}](https://tex.z-dn.net/?f=u%27%3D%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7Dc-%5Cfrac%7B1%7D%7B2%7Dc%7D%7B1-%5Cfrac%7B%5Cfrac%7B1%7D%7B3%7Dc%5Ctimes%20%5Cfrac%7B1%7D%7B2%7Dc%7D%7Bc%5E2%7D%7D)
or
![u'=\frac{\frac{5}{6}c}{1-\frac{1}{6}}](https://tex.z-dn.net/?f=u%27%3D%5Cfrac%7B%5Cfrac%7B5%7D%7B6%7Dc%7D%7B1-%5Cfrac%7B1%7D%7B6%7D%7D)
or
![u'=\frac{5}{7}c](https://tex.z-dn.net/?f=u%27%3D%5Cfrac%7B5%7D%7B7%7Dc)
since,
is less than (
), this means that the bullet will not hit