Question

A bullet travelling at a very high speed strikes a tree and gets stuck in it. In this process , it's momentum changes from 500kg m/s to zero in 5 seconds . The retarding force exerted by the tree on the bullet in this process would be -

1. 40N
2. 50N
3. 100N
4. 120N​
please help me

Answer 1

$\huge{\underline{\underline{\sf{Answer \colon}}}}$

From the Question,

• Inital Momentum,mu = 500Kg m/s

• Final Momentum,mv = 0Kg m/s

• Total Time,t = 5 sec

From Newton's II Law,

$\huge{\boxed{\sf{f = \frac{ \Delta{p}}{t} }}}$

We Know that,

$\sf{\Delta{P} = {P}_{f} - {P}_{I}} \\ \\ \implies \ \sf{\Delta{P} = mv - mu} \\ \\ \implies \ \sf{\Delta{P} = - 500Kgm{s}^{-1}}$

Now,

$\sf{f = \frac{-500}{5} } \\ \\ \huge{\rightarrow \: \sf{f = -100N}}$

Considering the magnitude of the repulsive force:

| f | = | -100 | = 100N

Thus,the force felt by the bullet due to the tree is 100N_____________(Option 3)

Answer 2

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

$\large{P_i = 500 \: kg m/s}$

$\large{P_f = 0 \:kg m/s}$

t = 5 seconds.

$\huge{\bold{\underline{Explanation:-}}}$

As we know,

$\huge{\bold{F = \frac{ \Delta P}{t}}}$

So, we need to find the change in momentum.

$\large{\bold{ \Delta P = P_f - P_i}}$

Substituting the values.

$\large{ \Delta P = 0 - 500}$

$\large{ \Delta P = - 500 kgm/s}$

Substituting in Force Formula.

$\large{\bold{F = \frac{ \Delta P}{t}}}$

$\large{ \to F = \frac{ - 500}{5}}$

$\large{ \to F = \frac{ \cancel{ - 500}}{ \cancel{5}}}$

$\large{ \to F = - 100 N}$

Taking only magnitude.

$\huge{\boxed{\boxed{F = 100 N}}}$

So, retardating force which acts on bullet is 100N

Therefore Option- 3 is correct.