Question

A body is projected from the ground with a velocity $v=(3\hat{i}+10\hat{j})m{s}^{-1}$ The maximum height attained and the range of the body respectively are (given $g=10m{s}^{-2}$)

• A. $5m$ and $6m$
• B. $3m$ and $10m$
• C. $6m$ and $5m$
• D. $3m$ and $5m$

Answer 1

Answer: (A)

$5m$ and $6m$

Velocity of projectile $v=3\hat{i}+10\hat{j}$ $m/s$

Speed of projectile $u=|v|=\sqrt{{10}^2+3^2}=\sqrt{109}$ $m/s$

Angle of projectile $\tan \theta =\frac{10}{3}$

$⟹$ $\sin \theta =\frac{10}{\sqrt{109}}$ and $\cos \theta =\frac{3}{\sqrt{109}}$

Maximum height attained $H=\frac{u^2{\sin }^2\theta }{2g}$

$\therefore$ $H=\frac{109\times \frac{100}{109}}{2\left(10\right)}=5m$

Horizontal range $R=\frac{u^2\sin 2\theta }{g}=\frac{2u^2\sin \theta \cos \theta }{g}$

$⟹$ $R=\frac{2\left(109\right)\times \frac{10}{\sqrt{109}}\times \frac{3}{\sqrt{109}}}{10}=6m$