Initial velocity (u) = 150 m/s
Final velocity (v) = 0 (since the bullet finally comes to rest)
Time taken to come to rest (t) = 0.03 s
The distance of penetration of the bullet into the block. Also the magnitude of the force exerted by the wooden block on the bullet.
According to the first equation of motion,
v= u + at
Acceleration of the bullet (a)
0 = 150 + (a — 0.03 s)
a = -150 / 0.03
a = – 5000 m/s2
Here the negative sign indicates that the velocity of the bullet is decreasing.
According to the third equation of motion,
v2= u2+ 2as
0 = (150)2+ 2 (-5000)
s = 22500 / 10000
s = 2.25 m
Hence, the distance of penetration of the bullet into the block is 2.25 m.
From Newton’s second law of motion,
Force (F) = Mass × Acceleration
Mass of the bullet (m) = 10 g
m = 0.01 kg
Acceleration of the bullet (a) = 5000 m/s2
F = m × a
F = 0.01× -5000
F = -50 N
Hence, the magnitude of the force exerted by the wooden block on the bullet is 50 N.