Question

A bullet of mass 10 g travelling horizontally with a velocity of
150 ms strikes a stationary wooden block and comes to rest
in 0.03 s. Calculate the distance of penetration of the bullet
into the block. Also calculate the magnitude of the force exerted
by the wooden block or the bullet.​

Answer 1

A bullet of mass 10 g travelling horizontally with a velocity of 150 m/s.

(mass of bullet is 10 g and initial velocity of the bullet is 150 m/s).

Also given that, the bullet strikes a stationary wooden block & comes to rest in 0.03 seconds. As, the bullet comes to rest. So the final velocity of the bullet is 0 m/s.

Using the First Equation Of Motion,

v = u + at

Substitute the values,

0 = 150 + a(0.03)

-150 = 0.03a

-5000 = a

So, the acceleration of the bullet is -5000 m/s².

Now,

Using the Third Equation Of Motion,

v² - u² = 2as

Substitute the known values,

(0)² - (150)² = 2(-5000)(s)

- 22500 = -10000s

225 = 100s

2.25 = s

So, the distance covered by the bullet is 2.25 m.

Also,

Force = mass × acceleration

(mass = 10g = 10/1000 = 0.01 kg)

Force = 0.01 × (5000)

Force = 50 N

Therefore, the Force exrerted by wooden block on bullet is 50N.

Answer 2

Given:-

• Mass (m) of bullet = 10g =10/1000=1/100 kg.

• Initial velocity (u) of bullet = 150 m/s

• Final velocity (v) of bullet = 0m/s (as it strike the wooden blocks and stopped) .

• Time (t) taken = 0.03 s

To Find:-

• Distance of penetration of the bullet.

• Magnitude of the force (F) exerted by the wooden blocks or the bullet.

Solution :-

Firstly we have to calculate the acceleration of bullet.

So By using 1st equation of motion

➦v = u + at

0 = 150 + a × 0.03

a × 0.03 = 150

a = 150 × 100/3 (0.03 change into fractions)

a = 5000 m/s²

and now by using 3rd equation of motion

➦ v ²= u² +2as

putting all the values which is given above

0² = 150² + 2× 5000 × s

0 = 22500 + 10000 × s

10000 × s = 22500

s = 22500/10000

s = 2.25m

∴ Distance of penetration of the bullet is 2.25m.

and Now, we have to calculate the magnitude of force .

➦ Force = mass × acceleration

F = m × a

F = 1/100 × 5000

F = 5000/100

F = 50 N

∴ The magnitude of force exerted by wooden blood or the bullet is 50 N.