Question

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The
angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30º. Find the distance travelled by the balloon during the interval.​

Answer 1

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

⎟⎟ ✪✪ ＱＵＥＳＴＩＯＮ ✪✪⎟⎟

A 1.2 ᴍ ᴛᴀʟʟ ɢɪʀʟ sᴘᴏᴛs ᴀ ʙᴀʟʟᴏᴏɴ ᴍᴏᴠɪɴɢ ᴡɪᴛʜ ᴛʜᴇ ᴡɪɴᴅ ɪɴ ᴀ ʜᴏʀɪᴢᴏɴᴛᴀʟ ʟɪɴᴇ ᴀᴛ ᴀ ʜᴇɪɢʜᴛ ᴏғ 88.2 ᴍ ғʀᴏᴍ ᴛʜᴇ ɢʀᴏᴜɴᴅ. Tʜᴇ ᴀɴɢʟᴇ ᴏғ ᴇʟᴇᴠᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ʙᴀʟʟᴏᴏɴ ғʀᴏᴍ ᴛʜᴇ ᴇʏᴇs ᴏғ ᴛʜᴇ ɢɪʀʟ ᴀᴛ ᴀɴʏ ɪɴsᴛᴀɴᴛ ɪs 60°. Aғᴛᴇʀ sᴏᴍᴇᴛɪᴍᴇ, ᴛʜᴇ ᴀɴɢʟᴇ ᴏғ ᴇʟᴇᴠᴀᴛɪᴏɴ ʀᴇᴅᴜᴄᴇs ᴛᴏ 30º. Fɪɴᴅ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ ʙʏ ᴛʜᴇ ʙᴀʟʟᴏᴏɴ ᴅᴜʀɪɴɢ ᴛʜᴇ ɪɴᴛᴇʀᴠᴀʟ.

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

⎟⎟ ✰✰ ＡＮＳＷＥＲ ✰✰ ⎟⎟

✿✿ ʀᴇғᴇʀ ᴛᴏ ɪᴍᴀɢᴇ ғɪʀsᴛ ✿✿

◆ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ʙᴀʟʟᴏᴏɴ ғʀᴏᴍ ᴛᴏᴡᴇʀ=88.2m

◆ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ɢɪʀʟ = 1.2 m

◆ ᴀɴɢʟᴇs ᴏғ ᴇʟᴇᴠᴀᴛɪᴏɴs = 60° ᴀɴᴅ 30°

◆ ʟᴇᴛ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ = d m

ғʀᴏᴍ ᴛʜᴇ ғɪɢᴜʀᴇ

tan 60° = 87/x

➜ √3 = 87/x

➜ 87 = √3 x ━━━━ ➀

➜ x = 87/√3 m

ᴀʟsᴏ tan 30° = 87/x+d

➜ 1/√3 = 87/x+d

➜ 87 = x+d/√3 ━━━━ ➁

ғʀᴏᴍ ➀ ᴀɴᴅ ➁

➜ √3x = x+d/√3

➜ √3 ᐧ √3x = x + d

➜ 3x = x + d

➜ 2x =d

ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ = 2 × 87/√3

➜ 2×29×√3×√3 / √3

➜ 58√3 m

.°. The distance travelled by the balloon during the interval = 58√3 m

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬