Question

A particle is thrown vertically upward with
velocity 20 m/s. Velocity of the particle when
it would be at half of its maximum height, is
​

Answer 1

Answer :

• The velocity of the particle at the half of the maximum height, u = 10√2 m/s.

Explanation :

Given :

• Initial velocity of the particle, u = 20 m/s.
• Final velocity of the particle, v = 0 m/s (Since at the maximum height the v is 0)
• Acceleration due to gravity, g = (-10) m/s².(Since the body is moving against the gravity the acceleration due to gravity is taken as negative)

To find :

• The velocity of the particle at the half of the maximum height, v = ?

Knowledge required :

Third equation of motion :

⠀⠀⠀⠀⠀⠀⠀⠀⠀v² = u² - 2gh⠀

Where,

• v = Final Velocity of the body.
• u = Initial velocity of the body.
• g = Acceleration due to gravity.
• h = Height of the body.

Solution :

To find the maximum hieght reached by the particle :

⠀By using the third equation of motion and substituting the values in it, we get :

⠀⠀=> v² = u² - 2gh

⠀⠀=> 0² = 20² - 2 × 10 × h

⠀⠀=> 0 = - 400 - 20h

⠀⠀=> -400/-20 = h

⠀⠀=> 20 = h

⠀⠀⠀∴ h = 20 m

Hence the maximum hieght reached by the particle is 20 m.

To find the velocity of the particle at the half of the maximum height :

⠀By using the third equation of motion and substituting the values in it, we get :

⠀⠀=> v² = u² - 2gh/2 [Since the height is Halved]

⠀⠀=> 0² = u² - 2 × 10 × 20/2

⠀⠀=> -u² = - 2 × 10 × 10

⠀⠀=> -u² = -200

⠀⠀=> u = √200

⠀⠀=> u = 10√2

⠀⠀⠀∴ u = 10√2 m/s

Therefore,

• The velocity of the particle at the half of the maximum height, u = 10√2 m/s

Answer 2

Qᴜᴇsᴛɪᴏɴ:-

➨ᴀ ᴘᴀʀᴛɪᴄʟᴇ ɪs ᴛʜʀᴏᴡɴ ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴜᴘᴡᴀʀᴅ ᴡɪᴛʜ ᴠᴇʟᴏᴄɪᴛʏ 20ᴍ/s.ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ᴘᴀʀᴛɪᴄʟᴇ ᴡʜᴇɴ ɪᴛ ᴡᴏᴜʟᴅ ʙᴇ ᴀᴛ ᴛʜᴇ ʜᴀʟғ ᴏғ ɪᴛs ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ ɪs

Aɴsᴡᴇʀ:-

➨ᴛᴏ ғɪɴᴅ:-

ᴛʜᴇ ᴠᴇʟᴏᴄɪᴛʏ ᴀɴᴅ ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ.

➨sᴏʟᴜᴛɪᴏɴ:-

ʙʏ ᴀᴘᴘʟʏɪɴɢ ᴛʜɪʀᴅ ᴇǫᴜᴀᴛɪᴏɴ ᴏғ ᴍᴏᴛɪᴏɴ:-

2ᴀs=ᴠ²-ᴜ²

2×(-20)×5=0²-20²

-40s= -400

s= 10ᴍ/s

ᴡᴇ ᴛᴀᴋᴇ ᴛʜᴇ ʜᴀʟғ sᴏ ᴛʜᴇ ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ ɪs 2×10=20ᴍ.

ʜᴇɴᴄᴇ ᴛʜᴇ ᴍᴀxɪᴍᴜᴍ ɪs 20ᴍ

➨ғɪɴᴅɪɴɢ ᴠᴇʟᴏᴄɪᴛʏ

ʙʏ ᴀᴘᴘʏɪɴɢ ɴᴇᴡᴛᴏɴ ᴛʜɪʀᴅ ʟᴀᴡ ᴏғ ᴍᴏᴛɪᴏɴ

ᴠ²=ᴜ²-2ɢʜ/2

0²=ᴜ²-2×10×20/2

0=ᴜ²-200

-ᴜ²= -200

ᴜ=√200

ᴜ= 10√2ᴍ/s

sᴏ ᴛʜᴇ ᴠᴇʟᴏᴄɪᴛʏ ɪs 10√2ᴍ/s ᴀɴᴅ ᴛʜᴇ ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ ɪs 20ᴍ.

ᴀɴᴅ ᴀʟʟ ᴡᴇ ᴀʀᴇ ᴅᴏɴᴇ✔️

ʜᴏᴘᴇ ɪᴛs ʜᴇʟᴘs ᴜʜ❣️