Question

A bullet of 10 g strikes a sand-bag at a speed of 103 m/s and gets embedded after travelling 5 cm. Calculate (i) the resistive force exerted by the sand on the bullet (ii) the time taken by the bullet to come to rest.

Answer 1

a = -u² / (2 S) ……[∵ v = 0]
= -(10³ m/s)² / (2 × 0.05 m)
= -10⁷ m/s²

F = ma
= (10 × 10^-3 kg) × (-10⁷ m/s²)
= -10⁵ N
Here negative sign indicates that Force acting is in opposite direction of bullet.
∴ Resistive Force exerted by bullet is 10⁵ N (or) 100 kN

v = u + at
0 = (10³ m/s) + (-10⁵ m/s² × t)
t = 0.01 second
∴ Time taken by bullet to come to rest is 0.01 second (or) 10 milliseconds.