Question

A hovering helicopter drops food packets from an altitude of 200 m towards passenger of a stranded boat

affected with flood. Each packet is of mass 500 gm. It is packed so well that it can withstand a momentum

upto 60 Ns. Find out which of the following is correct:

(A) The packet will break since the momentum of packet on reaching the

surface is more than 60 Ns.

(B) The packet will not break since its momentum on reaching the surface is

less than 40 Ns.

(C) the packet will break since its momentum on reaching the surface is 50 Ns.

(D) The packet will not break since its momentum on reaching the surface is 50

Ns.

ANSWER WITH BEST EXPLANATION WILL BE MARKED AS BRAINLIEST....

This question is from NTSE Stage-1 2015..... GL

Answer 1

Given:

A hovering helicopter drops food packets from an altitude of 200 m towards passenger of a stranded boat affected with flood. Each packet is of mass 500 gm. It is packed so well that it can withstand a momentum upto 60 Ns.

To find:

Correct statement among the following ?

Calculation:

Let velocity when the packet reaches ground be "v":

$\therefore \: {v}^{2} = {u}^{2} + 2gh$

$\implies \: {v}^{2} = {(0)}^{2} + 2(10)(200)$

$\implies \: {v}^{2} = 20 \times 200$

$\implies \: {v}^{2} = 4000$

$\implies \: v = \sqrt{4000}$

$\implies \: v = 63.24 \: m/s$

So, momentum of each packet:

$\therefore \: P = m \times v$

$\implies \: P = \dfrac{500}{1000} \times 63.24$

$\implies \: P = \dfrac{1}{2} \times 63.24$

$\implies \: P = 31.62 \: Ns$

$\implies \: P < 40\: Ns$

So, packets will not break because the final momentum will be less than 40 Ns.

Hope It Helps.