Question

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A balloon is ascending at the rate of 4.9m/s. A pocket is dropped from the balloon when situated at a height of 245m. How long does it take the packet to reach the ground? What is its final velocity?

Answer 1

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ɪɴɪᴛɪᴀʟʟʏ ᴛʜᴇ ᴘᴀᴄᴋᴇᴛ ᴡᴀꜱ ᴀꜱᴄᴇɴᴅɪɴɢ ᴜᴘ ᴡɪᴛʜ ᴛʜᴇ ʙᴀʟʟᴏᴏɴ.

ᴛᴀᴋɪɴɢ ᴜᴘᴡᴀʀᴅ ᴀꜱ ᴘᴏꜱɪᴛɪᴠᴇ ᴅɪʀᴇᴄᴛɪᴏɴ;

ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ, ᴜ = 4.9 ᴍ/ꜱ

ꜰɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ = ᴠ ᴍ/ꜱ

ɪɴɪᴛɪᴀʟ ʜᴇɪɢʜᴛ, ʜ₁ = 245 ᴍ  

ꜰɪɴᴀʟ ʜᴇɪɢʜᴛ, ʜ₂ = 0

ᴀ = -9.8 ᴍ/ꜱ²

ᴛɪᴍᴇ ᴛᴀᴋᴇɴ = ᴛ ꜱᴇᴄᴏɴᴅꜱ

ꜱ = ᴜᴛ + 0.5ᴀᴛ²

⇒ (ʜ₂-ʜ₁) = ᴜᴛ + 0.5ᴀᴛ²

⇒ 0-245 = 4.9ᴛ + 0.5×(-9.8)×ᴛ²

⇒ -245 = 4.9ᴛ - 4.9ᴛ²

⇒ 4.9ᴛ² -4.9ᴛ -245 =0

ꜱᴏʟᴠɪɴɢ ɪᴛ, ᴡᴇ ɢᴇᴛ  ᴛ = 7.59ꜱ

ᴠ = ᴜ + ᴀᴛ = 4.9 -9.8×7.59 = 4.9 - 74.38 = -69.48 ᴍ/ꜱ

ꜱᴏ ᴠᴇʟᴏᴄɪᴛʏ ɪꜱ 69.48 ᴍ/ꜱ ᴅᴏᴡɴᴡᴀʀᴅ

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Answer 2

U = 4.9 m/s

t = time to travel a total displacement of s= -245 m.

g = 9.8m/s^2

-245 = 4.9 t - 1/2× 9.8 × t^2

t^2 - t - 50 = 0

t = 0.5 + sqrt(50.25) sec.