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  4. A particle is projected with speed 20 m s- 1 at an angle 30° with horizontal. After how much time the angle between velocity and acceleration will be 90°

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Q. A particle is projected with speed $20 \, m \, s^{- 1}$ at an angle $30^\circ $ with horizontal. After how much time the angle between velocity and acceleration will be $90^\circ $

NTA AbhyasNTA Abhyas 2020Motion in a Plane

Solution:

Acceleration $g$ is vertically downward
To make velocity perpendicular to acceleration, velocity must be horizontal. This is possible at maximum height.
For this
$v_{y}=0$
$u_{y}=usin \theta $
$u_{y}=20sin30^\circ =10 \, m \, s^{- 2}$
$g=-10 \, ms^{- 2}$
We know that
$v_{y}=u_{y}+gt$
By putting all value, we get $t=1 \, \text{s}$