Question

a stone Falls from 90 metre height if its total potential energy conversion to kinetic energy calculate the velocity with which stone strikes the ground.please give proper answer. don't write anything u want ​

Answer 1

$\huge\mathfrak{Bonjour!!}$

$\huge\fcolorbox{black}{aqua}{Answer:-}$

✒ ᴛʜɪs ϙᴜᴇsᴛɪᴏɴ ɪs sᴜᴘᴇʀ ᴇᴀsʏ ɪғ ʏᴏᴜ ᴋɴᴏᴡ ᴀ ʙɪᴛ ᴏғ ᴋɪɴᴇᴍᴀᴛɪᴄs… ɪғ ʏᴏᴜ ᴋɴᴏᴡ ᴇϙᴜᴀᴛɪᴏɴs ᴏғ ᴍᴏᴛɪᴏɴ. sɪɴᴄᴇ ʏᴏᴜ’ʀᴇ ᴀsᴋɪɴɢ ᴛʜɪs, ɪ'ʟʟ ᴀssᴜᴍᴇ ʏᴏᴜ ʜᴀᴠᴇɴ'ᴛ ʙᴇᴇɴ ᴛᴀᴜɢʜᴛ ᴋɪɴᴇᴍᴀᴛɪᴄs. sᴏ… ʜᴏᴡ ᴛᴏ ғɪɢᴜʀᴇ ᴛʜɪs ᴏᴜᴛ ғʀᴏᴍ sᴄʀᴀᴛᴄʜ? (ᴡᴇ’ʟʟ sᴛɪʟʟ ɴᴇᴇᴅ ᴛᴏ ᴋɴᴏᴡ sᴏᴍᴇ ʙᴀsɪᴄ ᴀʟɢᴇʙʀᴀ.)

___________________________

ᴛʜᴇ sᴘʟɪᴛ sᴇᴄᴏɴᴅ ᴛʜᴀᴛ ᴡᴇ ғɪʀsᴛ ʟᴇᴛ ɢᴏ ᴏғ ᴛʜᴇ sᴛᴏɴᴇ, ɪᴛ’ʟʟ ʜᴀᴠᴇ ɴᴏ sᴘᴇᴇᴅ ᴀᴛ ᴀʟʟ. sᴏ ɪᴛs ɪɴɪᴛɪᴀʟ sᴘᴇᴇᴅ, ʟᴇᴛ’s ᴄᴀʟʟ ɪᴛ ᴜ, ɪs ᴢᴇʀᴏ, ɪ.ᴇ. ᴜ = 0 ᴍ/s.

ᴀs ᴛʜᴇ sᴛᴏɴᴇ ɪs ғᴀʟʟɪɴɢ, ɪᴛ’ʟʟ sᴘᴇᴇᴅ ᴜᴘ ᴅᴜᴇ ᴛᴏ ɢʀᴀᴠɪᴛʏ. ʟᴇᴛ's ᴄᴀʟʟ ᴛʜᴀᴛ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɢ. ᴏɴ ᴛʜᴇ ᴇᴀʀᴛʜ’s sᴜʀғᴀᴄᴇ (ɪ.ᴇ. ᴀᴛ sᴇᴀ ʟᴇᴠᴇʟ) ᴀɴᴅ ᴇᴠᴇɴ 90 ᴍ ᴀʙᴏᴠᴇ ɪᴛ, ɪᴛ'ʟʟ ʙᴇ ʀᴏᴜɢʜʟʏ ᴛʀᴜᴇ ᴛʜᴀᴛ ᴛʜᴇ ғʀᴇᴇ ғᴀʟʟɪɴɢ sᴛᴏɴᴇ ᴡɪʟʟ sᴘᴇᴇᴅ ᴜᴘ ʙʏ 9.81 ᴍ/s ᴇᴀᴄʜ sᴇᴄᴏɴᴅ. (ʏᴏᴜ ᴄᴀɴ ʟᴏᴏᴋ ᴜᴘ ᴛʜɪs ᴠᴀʟᴜᴇ ᴏɴʟɪɴᴇ.) ɪɴ sʜᴏʀᴛ, ɪᴛs ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪs ʀᴏᴜɢʜʟʏ ᴀ sᴛᴇᴀᴅʏ, ᴜɴᴄʜᴀɴɢɪɴɢ:

ɢ = 9.81 ᴍ/s ᴇᴠᴇʀʏ sᴇᴄᴏɴᴅ.

ɪɴ ᴏᴛʜᴇʀ ᴡᴏʀᴅs, ᴀғᴛᴇʀ 1 sᴇᴄᴏɴᴅ, ᴛʜᴇ sᴛᴏɴᴇ’s ғɪɴᴀʟ sᴘᴇᴇᴅ, ᴠ, ᴡᴏᴜʟᴅ ʙᴇ ᴠ =(9.81 × 1) ᴍ/s.

ᴀғᴛᴇʀ 2 sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ’s sᴘᴇᴇᴅ ᴡᴏᴜʟᴅ ʙᴇ ᴠ = (9.81 × 2) ᴍ/s.

ᴀғᴛᴇʀ 3 sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ’s sᴘᴇᴇᴅ ᴡᴏᴜʟᴅ ʙᴇ ᴠ = (9.81 × 3) ᴍ/s.

ɪɴ ɢᴇɴᴇʀᴀʟ, ᴀғᴛᴇʀ ᴛ sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ’s sᴘᴇᴇᴅ ᴡᴏᴜʟᴅ ʙᴇ ᴠ = 9.81 × ᴛ = ɢᴛ.

sɪɴᴄᴇ ᴠ = ɢᴛ, ᴛʜᴇɴ ᴛ = ᴠ/ɢ. ʟᴇᴛ’s ᴄᴀʟʟ ᴛʜɪs ᴇϙᴜᴀᴛɪᴏɴ (1).

ʟᴇᴛ’s ᴄᴀʟʟ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ ʙʏ ᴛʜᴇ sᴛᴏɴᴇ x. ɪғ ᴛʜᴇ sᴛᴏɴᴇ ᴡᴀs ᴍᴏᴠɪɴɢ ᴀᴛ ᴀ ᴄᴏɴsᴛᴀɴᴛ sᴘᴇᴇᴅ, ɪ.ᴇ. ɪғ ᴠ ᴡᴀs ᴄᴏɴsᴛᴀɴᴛ ᴀɴᴅ ɢ ᴡᴀs 0, ᴛʜᴇɴ:

ᴀғᴛᴇʀ 1 sᴇᴄᴏɴᴅ, ᴛʜᴇ sᴛᴏɴᴇ ᴡᴏᴜʟᴅ ʜᴀᴠᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ x = (ᴠ × 1) ᴍ.

ᴀғᴛᴇʀ 2 sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ ᴡᴏᴜʟᴅ ʜᴀᴠᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ x = (ᴠ × 2) ᴍ.

ᴀғᴛᴇʀ 3 sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ ᴡᴏᴜʟᴅ ʜᴀᴠᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ x = (ᴠ × 3 )ᴍ.

ɪɴ ɢᴇɴᴇʀᴀʟ, ᴀғᴛᴇʀ ᴛ sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ ᴡᴏᴜʟᴅ ʜᴀᴠᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ x = ᴠᴛ.

ʙᴜᴛ ᴡᴇ ᴋɴᴏᴡ ғʀᴏᴍ ᴇᴀʀʟɪᴇʀ ᴛʜᴀᴛ ᴛʜᴇ sᴛᴏɴᴇ ᴋᴇᴇᴘs sᴘᴇᴇᴅɪɴɢ ᴜᴘ ᴀs ɪᴛ ғᴀʟʟs, ɪ.ᴇ. ᴠ ɪs ɴᴏᴛ ᴄᴏɴsᴛᴀɴᴛ. sᴏ ᴡᴇ ᴄᴏᴜʟᴅ ɪɴsᴛᴇᴀᴅ ʟᴏᴏᴋ ᴀᴛ ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ, ʟᴇᴛ’s ᴄᴀʟʟ ɪᴛ <ᴠ>, ᴀɴᴅ sᴀʏ:

ᴀғᴛᴇʀ ᴛ sᴇᴄᴏɴᴅs, ᴛʜᴇ sᴛᴏɴᴇ ᴡᴏᴜʟᴅ ʜᴀᴠᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ x = <ᴠ> × ᴛ. ʟᴇᴛ’s ᴄᴀʟʟ ᴛʜɪs ᴇϙᴜᴀᴛɪᴏɴ (2).

ᴄᴏᴍʙɪɴɪɴɢ (1) ᴀɴᴅ (2): x = <ᴠ> × ᴠ/ɢ. ʟᴇᴛ’s ᴄᴀʟʟ ᴛʜɪs ᴇϙᴜᴀᴛɪᴏɴ (3).

ᴡᴇ ᴋɴᴏᴡ ʙʏ ᴛʜᴇ ᴇɴᴅ, ᴛʜᴇ sᴛᴏɴᴇ ᴛʀᴀᴠᴇʟs ᴀ ᴅɪsᴛᴀɴᴄᴇ ᴏғ x = 90 ᴍ. ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ɪᴛ sᴘᴇᴇᴅs ᴜᴘ ʙʏ ɢ = 9.81 ᴍ/s ᴇᴀᴄʜ sᴇᴄᴏɴᴅ ᴛʜᴀᴛ ɪᴛ ғᴀʟʟs. ᴡᴇ ᴡᴀɴᴛ ᴛᴏ ғɪɴᴅ ɪᴛs ғɪɴᴀʟ sᴘᴇᴇᴅ, ᴠ, ᴊᴜsᴛ ʙᴇғᴏʀᴇ ɪᴛ ʜɪᴛs ᴛʜᴇ ɢʀᴏᴜɴᴅ. ᴛʜᴇ ᴏɴʟʏ ᴍɪssɪɴɢ ᴘɪᴇᴄᴇ ᴏғ ᴛʜᴇ ᴘᴜᴢᴢʟᴇ ɪɴ (3) ɪs ᴛʜᴇ sᴛᴏɴᴇ’s ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ, <ᴠ>.

ɪғ ᴡᴇ ʜᴀᴅ sᴇᴠᴇʀᴀʟ ʙᴏxᴇs ᴡɪᴛʜ ᴀ ᴅɪғғᴇʀᴇɴᴛ ɴᴜᴍʙᴇʀ ᴏғ ɪᴛᴇᴍs ɪɴ ᴇᴀᴄʜ ʙᴏx, ᴛᴏ ғɪɴᴅ ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ɴᴜᴍʙᴇʀ ᴏғ ɪᴛᴇᴍs ᴘᴇʀ ʙᴏx, ᴡᴇ’ᴅ ᴀᴅᴅ ᴜᴘ ᴀʟʟ ᴛʜᴇ ɪᴛᴇᴍs ᴀɴᴅ ᴅɪᴠɪᴅᴇ ᴛʜᴇ ᴛᴏᴛᴀʟ ʙʏ ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ʙᴏxᴇs. ᴇ.ɢ.: ɪғ ᴡᴇ ʜᴀᴅ 2 ʙᴏxᴇs ᴡɪᴛʜ 5 ᴀɴᴅ 3 ɪᴛᴇᴍs ᴇᴀᴄʜ, ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴡᴏᴜʟᴅ ʙᴇ (5 + 3)/2 = 4 ɪᴛᴇᴍs ᴘᴇʀ ʙᴏx.

sɪɴᴄᴇ ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪs ᴄᴏɴsᴛᴀɴᴛ, ᴡᴇ ᴄᴀɴ ᴜsᴇ ᴛʜᴇ sᴀᴍᴇ ᴍᴇᴛʜᴏᴅ ᴀs ᴛʜᴇ ɪᴛᴇᴍs ɪɴ ᴛʜᴇ ʙᴏxᴇs ᴛᴏ ғɪɴᴅ ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ, <ᴠ>. ᴡᴇ ᴊᴜsᴛ ᴛᴀᴋᴇ ᴛʜᴇ ɪɴɪᴛɪᴀʟ sᴘᴇᴇᴅ, ᴜ, ᴀɴᴅ ᴛʜᴇ ғɪɴᴀʟ sᴘᴇᴇᴅ, ᴠ, ᴀᴅᴅ ᴛʜᴇᴍ ᴜᴘ, ᴀɴᴅ ᴅɪᴠɪᴅᴇ ᴛʜᴇᴍ ʙʏ 2 ᴛᴏ ɢᴇᴛ:

<ᴠ> = (ᴜ + ᴠ)/2. ʙᴜᴛ ᴜ = 0. sᴏ, <ᴠ> = ᴠ/2. ʟᴇᴛ’s ᴄᴀʟʟ ᴛʜɪs ᴇϙᴜᴀᴛɪᴏɴ (4).

(ɴᴏᴛᴇ: ɪғ ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴡᴀsɴ’ᴛ ᴄᴏɴsᴛᴀɴᴛ, ғɪɴᴅɪɴɢ ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ sᴘᴇᴇᴅ ᴡᴏᴜʟᴅ ʙᴇ ᴍᴜᴄʜ ᴛʀɪᴄᴋɪᴇʀ. ᴡᴇ ᴡᴏᴜʟᴅɴ’ᴛ ʙᴇ ᴀʙʟᴇ ᴛᴏ ᴜsᴇ ᴛʜᴇ ᴇᴀsʏ ᴍᴇᴛʜᴏᴅ ᴀʙᴏᴠᴇ.)

ᴄᴏᴍʙɪɴɪɴɢ (3) ᴀɴᴅ (4): x = (ᴠ/2) × (ᴠ/ɢ) = (ᴠ^2)/2ɢ

sᴏ (ᴠ^2) = 2ɢx ᴀɴᴅ ᴠ = √(2ɢx)

sᴏ ᴛʜᴇ sᴛᴏɴᴇ’s ғɪɴᴀʟ sᴘᴇᴇᴅ ᴊᴜsᴛ ʙᴇғᴏʀᴇ ʜɪᴛᴛɪɴɢ ᴛʜᴇ ɢʀᴏᴜɴᴅ ɪs:

ᴠ = √(2 × 9.81 × 90) ᴍ/s = √(1765.8) ᴍ/s = 42.0 ᴍ/s.

___________________________

$<marquee>❤í հօթҽ Եհís հҽlթs!❤$