Question

A particle is projected from earth surface in vertically upwards direction. Kinetic energy of the particle is half of escape energy . How much height the particle will attain from earth surface

Answer 1

• ᴀ ᴘᴀʀᴛɪᴄʟᴇ ɪs ᴘʀᴏᴊᴇᴄᴛᴇᴅ ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴜᴘᴡᴀʀᴅ ғʀᴏᴍ ᴛʜᴇ sᴜʀғᴀᴄᴇ ᴏғ ᴇᴀʀᴛʜ (ʀᴀᴅɪᴜs \( ʀ_{ᴇ} \) ) ᴡɪᴛʜ ᴀ ᴋɪɴᴇᴛɪᴄ ᴇɴᴇʀɢʏ ᴇϙᴜᴀʟ ᴛᴏ ʜᴀʟғ ᴏғ ᴛʜᴇ ᴍɪɴɪᴍᴜᴍ ᴠᴀʟᴜᴇ ɴᴇᴇᴅᴇᴅ ғᴏʀ ɪᴛ ᴛᴏ ᴇsᴄᴀᴘᴇ. ᴛʜᴇ ʜᴇɪɢʜᴛ ᴛᴏ ᴡʜɪᴄʜ ɪᴛ ʀɪsᴇs ᴀʙᴏᴠᴇ ᴛʜᴇ sᴜʀғᴀᴄᴇ ᴏғ ᴇᴀʀᴛʜ ɪs. \( (1) ʜ=ʀ_{ᴇ} \) \( (2) ʜ=2 ʀ_{ᴇ} \).