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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Rest and Motion Kinematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rest and Motion Kinematics

During a projectile motion, the velocity

During a projectile motion, the velocity

Options

  1. Ais never perpendicular to the acceleration
  2. Bis perpendicular to the acceleration for a single instant only
  3. Cis always perpendicular to the acceleration
  4. Dis perpendicular to the acceleration for two distinct instants

Correct answer

B. is perpendicular to the acceleration for a single instant only

Step-by-step solution

In projectile motion, the acceleration is constant and acts vertically downwards, a⃗=−gj^\vec{a} = -g \hat{j}.

The velocity of the projectile at any instant tt is given by v⃗=ucos⁡θi^+(usin⁡θ−gt)j^\vec{v} = u \cos \theta \hat{i} + (u \sin \theta - gt) \hat{j}.

For velocity to be perpendicular to acceleration, their dot product must be zero.

v⃗⋅a⃗=0\vec{v} \cdot \vec{a} = 0

−g(usin⁡θ−gt)=0-g(u \sin \theta - gt) = 0

t=usin⁡θgt = \dfrac{u \sin \theta}{g}

This time corresponds to the highest point of the trajectory. Since there is only one such instant during the motion, the velocity is perpendicular to the acceleration for a single instant only.
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