Question

A 6 kg bomb at rest explodes into three equal pieces p q r and p flies with speed of 30 m per second and q with speed 40 m per second making an angle 90 degree with the direction of p

Answer 1

$\textsf{\red{Given!!}}$

$\textsf{\green{As no external force is present in our system.}}$

$\textsf{\orange{So Momentum is conserved:}}$

$\textsf{\blue{Momentum of particle P = 30 x 2 = 60 (i)}}$

$\textsf{\violet{Momentum of particle Q = 40 x 2 = 80 (j)}}$

$\textsf{\brown{Resultant of Momentum of particle P and Q will be equal to Momentum of particle R}}$

$\sf\implies\:So \:|R| \:= \:| P\: + \:Q | =\: \sqrt{ (60)^2 + (80)^2 + 2 PQ Cos 90}$

| R | = 100
| m v| = 100
|v| = 50 m/s
To Find angle b/w P & R
So, Again the resultant of P and R will be equal to Q:
Let the angle b/w P and R be Theta
Therefore
|Q|2 = |P|2+|R|2 + 2 PR Cos Theta
1600 = 900 + 2500 + 2 x 1500 x Cos Theta
then 
Cos theta = -(.6)
Theta = 127 Degree

Answer 2

Answer:

[ᴛᴇx]\ᴛᴇxᴛsғ{\ʀᴇᴅ{ɢɪᴠᴇɴ!!}}[/ᴛᴇx]

[ᴛᴇx]\ᴛᴇxᴛsғ{\ɢʀᴇᴇɴ{ᴀs ɴᴏ ᴇxᴛᴇʀɴᴀʟ ғᴏʀᴄᴇ ɪs ᴘʀᴇsᴇɴᴛ ɪɴ ᴏᴜʀ sʏsᴛᴇᴍ.}}[/ᴛᴇx]

[ᴛᴇx]\ᴛᴇxᴛsғ{\ᴏʀᴀɴɢᴇ{sᴏ ᴍᴏᴍᴇɴᴛᴜᴍ ɪs ᴄᴏɴsᴇʀᴠᴇᴅ:}}[/ᴛᴇx]

[ᴛᴇx]\ᴛᴇxᴛsғ{\ʙʟᴜᴇ{ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴘᴀʀᴛɪᴄʟᴇ ᴘ = x = (ɪ)}}[/ᴛᴇx]

[ᴛᴇx]\ᴛᴇxᴛsғ{\ᴠɪᴏʟᴇᴛ{ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴘᴀʀᴛɪᴄʟᴇ ǫ = x = (ᴊ)}}[/ᴛᴇx]

[ᴛᴇx]\ᴛᴇxᴛsғ{\ʙʀᴏᴡɴ{ʀᴇsᴜʟᴛᴀɴᴛ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴘᴀʀᴛɪᴄʟᴇ ᴘ ᴀɴᴅ ǫ ᴡɪʟʟ ʙᴇ ᴇǫᴜᴀʟ ᴛᴏ ᴍᴏᴍᴇɴᴛᴜᴍ ᴏғ ᴘᴀʀᴛɪᴄʟᴇ ʀ}}[/ᴛᴇx]

[ᴛᴇx]\sғ\ɪᴍᴘʟɪᴇs\:sᴏ \:|ʀ| \:= \:| ᴘ\: + \:ǫ | =\: \sǫʀᴛ{ ()^ + ()^ + ᴘǫ ᴄᴏs }[/ᴛᴇx]

| ʀ | =

| ᴍ ᴠ| =

|ᴠ| = ᴍ/s

ᴛᴏ ғɪɴᴅ ᴀɴɢʟᴇ ʙ/ᴡ ᴘ & ʀ

sᴏ, ᴀɢᴀɪɴ ᴛʜᴇ ʀᴇsᴜʟᴛᴀɴᴛ ᴏғ ᴘ ᴀɴᴅ ʀ ᴡɪʟʟ ʙᴇ ᴇǫᴜᴀʟ ᴛᴏ ǫ:

ʟᴇᴛ ᴛʜᴇ ᴀɴɢʟᴇ ʙ/ᴡ ᴘ ᴀɴᴅ ʀ ʙᴇ ᴛʜᴇᴛᴀ

ᴛʜᴇʀᴇғᴏʀᴇ

|ǫ| = |ᴘ|+|ʀ| + ᴘʀ ᴄᴏs ᴛʜᴇᴛᴀ

= + + x x ᴄᴏs ᴛʜᴇᴛᴀ

ᴛʜᴇɴ 

ᴄᴏs ᴛʜᴇᴛᴀ = -(.)

ᴛʜᴇᴛᴀ = ᴅᴇɢʀᴇᴇ