Concepts Of Physics MCQ Edition [Volume 1]PhysicsRest and Motion Kinematics
During a projectile motion, the velocity
Options
- Ais never perpendicular to the acceleration
- Bis perpendicular to the acceleration for a single instant only
- Cis always perpendicular to the acceleration
- 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, a = -g j . The velocity of the projectile at any instant t is given by v = u i + (u - gt) j . For velocity to be perpendicular to acceleration, their dot product must be zero. v a = 0 -g(u - gt) = 0 t = u 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.