For an object projected from ground with speed u horizontal range is two times the maximum height attained by it.The horizontal range of object is
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ʟᴇᴛ θ ʙᴇ ᴛʜᴇ ᴀɴɢʟᴇ ᴏғ ᴏʙᴊᴇᴄᴛ ғʀᴏᴍ ɢʀᴏᴜɴᴅ.
ɢɪᴠᴇɴ,
ʜᴏʀɪᴢᴏɴᴛᴀʟ ʀᴀɴɢᴇ = 2 × ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ
ᴜ2sɪɴ2θɢ = 2×ᴜ2sɪɴ2θ2ɢ 2 sɪɴθ ᴄᴏsθ = sɪɴ2θ ᴛᴀɴθ = 2 sᴏ, ᴄᴏsθ = 15√ sɪɴθ = 25√ ᴛʜᴇʀᴇғᴏʀᴇ,ʜᴏʀɪᴢᴏɴᴛᴀʟ ʀᴀɴɢᴇ, = ᴜ2sɪɴ2θɢ = 2ᴜ2 sɪɴθ ᴄᴏsθɢ = 45ᴜ2ɢ
ɢɪᴠᴇɴ,
ʜᴏʀɪᴢᴏɴᴛᴀʟ ʀᴀɴɢᴇ = 2 × ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ
ᴜ2sɪɴ2θɢ = 2×ᴜ2sɪɴ2θ2ɢ 2 sɪɴθ ᴄᴏsθ = sɪɴ2θ ᴛᴀɴθ = 2 sᴏ, ᴄᴏsθ = 15√ sɪɴθ = 25√ ᴛʜᴇʀᴇғᴏʀᴇ,ʜᴏʀɪᴢᴏɴᴛᴀʟ ʀᴀɴɢᴇ, = ᴜ2sɪɴ2θɢ = 2ᴜ2 sɪɴθ ᴄᴏsθɢ = 45ᴜ2ɢ
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