a bullet of mass 25 g is fired from a pistol at a velocity of 200 m/s. if mass of the pistol is 2.5 kg calculate its recoil velocity

Do this type of thing but change it a little bit. This is a conservation of momentum problem. The initial momentum of the system (gun + bullet) is zero, as neither is moving.
There fore, after the gun is fired, the total momentum must still be zero.
m
g
×
v
g
+
m
b
×
v
b
=
0
Inserting what we know:
(
0.025
)
(
210
)
+
(
0.91
)
v
b
=
o
v
b
=
−
(
0.025
)
(
210
)
0.91
=
−
5.8
m
s
The negative sign tells us that the gun travels in a direction opposite to that of the bullet.

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