Question

Q. 5 A bullet of 10 g strikes a sandbag at a speed of 103 ms-1 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

Answer:

(i) the resistive force exerted by the sand on the bullet is - 1 x 10⁵ N

(ii) the time taken by the bullet to come to rest is 1 x 10⁻⁴ s

Explanation:

Given;

mass of bullet, m = 10 g = 0.01 kg

speed of the bullet, v = 10³ m/s

distance traveled by the bullet, d = 5 cm = 0.05 m

(i) the resistive force exerted by the sand on the bullet

the acceleration of the bullet is given by;

v² = u² + 2as

0 = (10³)² + a(2 x 0.05)

-0.1a = (10⁶)

-a = (10⁶) / 0.1

a = -1 x 10⁷ m/s²

The resistive force is given by;

F = ma

F = (0.01)(-1 x 10⁷)

F = - 1 x 10⁵ N

(ii) the time taken by the bullet to come to rest.

v = u + at

0 = 10³ + (-1 x 10⁷ t)

1 x 10⁷ t = 10³

t = 10³  / 10⁷

t = 1 x 10⁻⁴ s