Question

A body is projected with a velocity $u$ making an angle $\theta$ with the horizontal. The time after which its vertical component of velocity is equal to horizontal component is

• A. $\frac{u}{g\sin \theta }$
• B. $\frac{u}{g}(\sin \theta -\cos \theta )$
• C. $\frac{u}{g\cos \theta }$
• D. $\frac{u}{g}(\cos \theta -\sin \theta )$

Answer 1

Answer: (B)

$\frac{u}{g}(\sin \theta -\cos \theta )$

Initial horizontal velocity $=u\cos \theta$
initial vertical velocity$=u\sin \theta$
$\because V_h=$final vertical velocity $=u\cos \theta$
$v=u+at$
$u\cos \theta =u\sin \theta -gt$
$\Rightarrow t=\frac{u}{g}(\sin \theta -\cos \theta )$