Question

A bullet of 10 g moving with a speed of 100 m/s penetrates a sandbag
and comes to rest in 1/10 th second Find
a) The distance through which the bullet penetrates
b) The retarding force experienced​

Answer 1

Answer:

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

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 = -5000 m/s2

(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)

= 22500 / 10000

= 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 = 0.01 kg

Acceleration of the bullet, a = 5000 m/s2

F = ma = 0.01 * 5000 = 50 N

Hence, the magnitude of the force exerted by the wooden block on the bullet is 50 N.

Answer 2

The answers are as follows;

The answers are as follows; (a) -10N

The answers are as follows; (a) -10N (b) 5 meters

GIVEN

A bullet of 10 g moving with a speed of 100 m/s penetrates a sandbag and comes to rest in 1/10 th second.

TO FIND

a) The distance through which the bullet penetrates

b) The retarding force experienced.

SOLUTION

We can simply solve the above problem as follows;

It is given,

Mass of the bullet = 10 grams = 0.01 kg

Initial velocity of bullet = 100m/s

Time taken = 1/10 = 0.1 second

Final velocity = 0

Applying the formula to calculate acceleration

v = u+at

0 = 100 + 0.01a

a = - 100/0.01 = - 1000m/s²

To calculate the retarding force, We will apply the following formula,

F = ma

Putting the values in the above formula we get,

F = 0.01 × - 1000m/s²

= -10N

Applying second equation of motion to calculate distance;

$s = ut + \frac{1}{2} a {t}^{2}$

=

$100 \times 0.1 + \frac{1}{2} \times - 1000 \times {0.1}^{2}$

= 10-5= 5 meters.

Hence, The answers are as follows;

• Hence, The answers are as follows; (a) -10N
• Hence, The answers are as follows; (a) -10N (b) 5 meters

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