Question

A bullet of 10g strike the sand bag at a speed of 100m/s and gets embedded after travelling 5cm.calculate
(a)Resistive force exerted by sand on bullet.
(b)Time taken by bullet to come to rest.​

Answer 1

Given:-

• Mass of Bullet = 10g → 0.01kg

• Initial Velocity of the bullet = 100m/s

• Distance covered = 5cm → 0.05m

• Final Velocity = 0m/s

To Find:-

• Force exerted by sand on bullet

• Time taken by bullet to come to rest.

Formulae used:-

• v² - u² = 2as

• F = ma

Where,

• v = Final Velocity

• u = Initial Velocity

• a = Acceleration

• s = Distance

Now,

→ v² - u² = 2as

→ (0)² - (100)² = 2 × a × 0.05

→ -10000 = 0.1a

→ a = -100000m/s²

Hence, The Acceleration is -100000m/s²

Therefore,

→ F = ma

→ F = 0.01 × -100000

→ F = -1000N

So, The Force exerted by sand on bullet is -1000N

Note :- Negative Sign implies force is acting opposite to the Direction.

Now,

→ v = u + at

→ (0) = 100 + -100000 × t

→ -100 = -100000t

→ t = 100/100000

→ t = 0.001s.

Hence, Time taken by bullet to come at rest is 0.001s.