Question

A body is projected with a velocity $v$, making an angle $\theta$ with the horizontal.What is the angle made by the resultant velocity with the horizontal, after one second from the start?

Answer 1

Given,

Projected velocity, $v$
angel, $\theta$

Velocity at any time $t$

$V_t=v\cos \theta \hat{i}+(v\sin \theta -gt)\hat{j}$

$\tan \alpha =\frac{v\sin \theta -gt}{v\cos \theta }$

$(att=1)\tan \alpha =\frac{v\sin \theta -g}{v\cos \theta }$

Angle at time 1 sec from start $\alpha ={\tan }^{-1}\left(\frac{v\sin \theta -g}{v\cos \theta }\right)$