A body is projected from the ground at an… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

2022integereasy

A body is projected from the ground at an angle of $45^{\circ}$ with the horizontal. Its velocity after $2s$ is $20{ms}^{-1}$ . The maximum height reached by the body during its motion is _____ $m$ . (use $g=10{ms}^{-2}$ )

Official previous-year question

Held on 24 Jun 2022 · Verified 6 Jul 2026.

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Solution

JEE Main 2022 Physics, Motion In Two Dimensions — solution figure

After $2s$ the velocity is $20m{s}^{-1}$

$\Rightarrow {v}_{x}^{2}+{v}_{y}^{2}={v}^{2}=400$

$\Rightarrow {u}^{2}{\mathrm{cos}}^{2}45^{\circ}+{(u\mathrm{sin}45^{\circ}-gt)}^{2}=\frac{{u}^{2}}{2}+{(\frac{u}{\sqrt{2}}-20)}^{2}=400$

$\Rightarrow \frac{{u}^{2}}{2}+\frac{{u}^{2}}{2}+400-\frac{40}{\sqrt{2}}u=400$

$\Rightarrow {u}^{2}=\frac{40}{\sqrt{2}}u\Rightarrow u=\frac{40}{\sqrt{2}}m{s}^{-1}$

Now the maximum height of the projectile is given by,

$H=\frac{{u}^{2}{\mathrm{sin}}^{2}\theta }{2g} \Rightarrow H=\frac{1600}{20\times 2\times 2}=20m$

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