A ball is dropped from a height of 2.50m above the floor. Find the speed V with which it reaches the floor. The ball now rebounds. The speed of ball is decreased to 3V/4 due to this collision. How high will the ball rise?
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✮❀ӇЄƦЄ ƖƧ ƳƠƲƦ ƛƝƧƜЄƦ❀✮
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[➊] ✮✮✮✮✮
Vo ➙ 0 m/s
H ➙ 2.5 m
g ➙ 9.8 m/s^2
V ➙ √(2gH)
...➙ √(2 × 9.8 × 2.5)
...➙ 7 m/s
[➋] ✮✮✮✮✮
(Kɪɴᴇᴛɪᴄ ᴇɴᴇʀɢʏ ᴏғ ʙᴀʟʟ ᴀғᴛᴇʀ ʟᴏꜱɪɴɢ ᴛʜᴇ ꜱᴏᴍᴇ ᴇɴᴇʀɢʏ ᴅᴜᴇ ᴛᴏ ᴄᴏʟʟɪꜱɪᴏɴ ᴀʀᴇ)
K➙ 0.5 mv^2
..➙ 0.5m × (3√/4)^2
..➙ 0.5m × (3 × 7/4)^2
..➙ 0.5m × (21 /4 )^2
(Tʜᴇɴ, Tʜɪꜱ ᴇɴᴇʀɢʏ ɪꜱ ᴄᴏɴᴠᴇʀᴛᴇᴅ ɪɴᴛᴏ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ᴀᴛ ʜᴇɪɢʜᴛ 'ʜ')
....➙ 0.5m × (21 /4 )^2 = mgh
H ➙ (21 /4 )^2 / (2g)
H ➙ (21 /4 )^2 / (2 × 9.8)
H ➙ 1.40 m...✔
Sᴏ, ᴛʜᴇ ʙᴀʟʟ ᴡɪʟʟ ʀɪꜱᴇ ᴛᴏ ᴛʜᴇ ʜᴇɪɢʜᴛ ɪꜱ ᴇϙᴜᴀʟ ᴛᴏ 1.40m.
✮❀ӇЄƦЄ ƖƧ ƳƠƲƦ ƛƝƧƜЄƦ❀✮
╰━─━─━─━─≪✠≫─━─━─━─━╯
[➊] ✮✮✮✮✮
Vo ➙ 0 m/s
H ➙ 2.5 m
g ➙ 9.8 m/s^2
V ➙ √(2gH)
...➙ √(2 × 9.8 × 2.5)
...➙ 7 m/s
[➋] ✮✮✮✮✮
(Kɪɴᴇᴛɪᴄ ᴇɴᴇʀɢʏ ᴏғ ʙᴀʟʟ ᴀғᴛᴇʀ ʟᴏꜱɪɴɢ ᴛʜᴇ ꜱᴏᴍᴇ ᴇɴᴇʀɢʏ ᴅᴜᴇ ᴛᴏ ᴄᴏʟʟɪꜱɪᴏɴ ᴀʀᴇ)
K➙ 0.5 mv^2
..➙ 0.5m × (3√/4)^2
..➙ 0.5m × (3 × 7/4)^2
..➙ 0.5m × (21 /4 )^2
(Tʜᴇɴ, Tʜɪꜱ ᴇɴᴇʀɢʏ ɪꜱ ᴄᴏɴᴠᴇʀᴛᴇᴅ ɪɴᴛᴏ ᴘᴏᴛᴇɴᴛɪᴀʟ ᴇɴᴇʀɢʏ ᴀᴛ ʜᴇɪɢʜᴛ 'ʜ')
....➙ 0.5m × (21 /4 )^2 = mgh
H ➙ (21 /4 )^2 / (2g)
H ➙ (21 /4 )^2 / (2 × 9.8)
H ➙ 1.40 m...✔
Sᴏ, ᴛʜᴇ ʙᴀʟʟ ᴡɪʟʟ ʀɪꜱᴇ ᴛᴏ ᴛʜᴇ ʜᴇɪɢʜᴛ ɪꜱ ᴇϙᴜᴀʟ ᴛᴏ 1.40m.
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