Try this beautiful 2D Motion Problem based on Projectile Motion from NSEP - 2019.
A particle is projected from the ground with a velocity $\vec{V}$=$(3 \hat{i}+10 \hat{j}) \mathrm{ms}^{-1}$. The maximum height attained and the range of the particle are respectively given by (use $\mathrm{g}$=$10 \mathrm{~m} / \mathrm{s}^{2}$ )
(a) $5 \mathrm{~m}$ and $6 \mathrm{~m}$
(b) $3 \mathrm{~m}$ and $10 \mathrm{~m}$
(c) $6 \mathrm{~m}$ and $5 \mathrm{~m}$
(d) $3 \mathrm{~m}$ and $5 \mathrm{~m}$
Kinematics
2 Dimensional Motion
Projectile Motion
Resnick Halliday Krane
NSEP 2019; Question no:26
(a) $5 \mathrm{~m}$ and $6 \mathrm{~m}$
Resolution of the Components of Vectors
For the Vertical journey which component of the Velocity is responsible for it
${H}=\frac{\mathrm{u}_{\mathrm{y}}^{2}}{2 \mathrm{~g}}=\frac{10^{2}}{20}=5 \mathrm{~m}$
Could we able to think about the relation between the Range and the horizontal component of Velocity
$R=u_{x} \frac{2 u_{y}}{g}=3 \times \frac{2 \times 10}{10}=6 \mathrm{~m}$
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