Question

please tell from which book is this question from
a stone projected vertically upwards takes 2.5 seconds to reach the highest point calculate the initial velocity of the stone maximum height attained by the stone take g as 9.8 metre per second ​​

Answer 1

✰Gɪᴠᴇɴ :-

ᴠ = ғɪɴᴀʟ ᴠᴇʟᴏᴠɪᴛʏ = 0 ᴍ/sᴇᴄ

g = 9.8 ᴍ/sᴇᴄ²

t = 2.5 sec

✰Tᴏ ғɪɴᴅ :-

ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ (ᴜ)

ᴍᴀxɪᴍᴜᴍ ʜᴇɪɢʜᴛ (s)

✰Sᴏʟᴜᴛɪᴏɴ :-

Bʏ 1sᴛ ᴋɪɴᴇᴍᴀᴛɪᴄᴀʟ ᴇǫᴜᴀᴛɪᴏɴ...

ᴠ = u - gt

0 = u - 9.8(2.5)

ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ = u = 24.5 m/sec

ʙʏ 2ɴᴅ ᴋɪɴᴇᴍᴀᴛɪᴄᴀʟ ᴇǫᴜᴀᴛɪᴏɴ....

s = ᴜt - (1/2)gt²

s = 24.5(2.5) - (1/2)(9.8)(2.5)²

s = 61.25 - (1/2)(9.8)(6.25)

s = 61.25 - 30.62

s = 30.62 metres

Hɪɢʜᴇsᴛ ᴘᴏɪɴᴛ ᴀᴛᴛᴀɪɴᴇᴅ = s = 30.62 ᴍᴇᴛʀᴇs

ᵐᵃʳᵏ ᵃˢ ᵇʳᵃⁱⁿˡⁱᵉˢᵗ.....✌️✌️

Answer 2

We have,

Time, t = 2.5 s

Final velocity, v = 0 m/s {Becomes rest due to gravity}

Acceleration (due to gravity) = - 9.8 m/s² {Upward}

We know,

v = u ± gt

⇒0 = u - gt

⇒u = gt

⇒u = (9.8 m/s²)(2.5 s) = 24.5 m/s ...(1)

Also,

v² - u² = ± 2gh

⇒0 = u² - 2gh

⇒h = u²/2g

⇒h = (24.5 m/s)²/(2 × 9.8 m/s²)

⇒h = 30.625 m ...(2)