A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height h…
JEE Main 2022 — Physics Mechanics
2022mcqmedium
A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height 3h while going up and coming down respectively.
Official previous-year question
Held on 29 Jul 2022 · Verified 6 Jul 2026.
Options
A
2+12−1
B
3+23−2
C
3+13−1
D
31
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Solution
The maximum height of a projectile thrown vertically upward is given by, h=2gu2.
⇒u=2gh
Using equation of motion with constant acceleration,
s=ut+21at2
⇒3h=2ght−21gt2
⇒2gt2−2ght+3h=0
Solving the above quadratic equation we will get the times t1 and t2. ⇒t1t2=2gh−2gh−4×2g×3h2gh+2gh−4×2g×3h=2gh−34gh2gh+34gh=3−23+2
Thus, the ratio t2t1=3+23−2
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