Question

A particle is projected from ground with a velocity of 40 m/s making an angle of 30^o with horizontal. Then

Moderate

A

After 2 sec, its velocity vector will be perpendicular to the initial velocity vector.
B

After 3 sec, its velocity vector will be perpendicular to the initial velocitylk vector.
C

After 3.5 sec, its velocity vector will be perpendicular to the initial velcoity vector.
D

Velocity vector of the particle will never be perpendicular to the initial velocity vector.

Solution

Velocity vector will be perpendicular to a the initial velocity vector if angle of projection is greater than 45^o.
Since $\vec{u}$ is perpendicular to $\vec{V}, \vec{u} . \vec{v} = 0$
i.e. $(u \cos α \hat{i} + u \sin α \hat{j}) . [u \cos α \hat{i} + (u \sin α - g t) \hat{j}] = 0$
$\Rightarrow t = \frac{u}{g \sin α}$
Now $t > T \Rightarrow \frac{u}{g \sin α} > \frac{2 u \sin α}{g} \Rightarrow α < 45^{o}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME