Question

The acceleration and velocity of a projectile in plane to plane projectile motion are always perpendicular to each other.

• A. True
• B. False

Answer 1

The correct option is B False

Projectile motion:

The diagrammatic representation of the projectile motion of a projectile is given below:

1. Here, $u$ is the velocity of the projectile, $u_x$ is the horizontal component and $u_y$ is the vertical component of the velocity of the projectile at an instant.
2. Here, $\theta$is the angle of projection and $A$ is the point where the projectile has the maximum height.
3. The only acceleration acting on the projectile is gravity. Hence, the direction of acceleration will be downwards. The downward direction is considered a negative direction here.

Maximum Height:

1. The direction of gravity (acceleration) is downwards throughout the projectile motion. If we want gravity to be perpendicular to the velocity of the projectile then the velocity should be parallel to the x-axis.

2. The velocity of the projectile is parallel to the x-axis only when it is at the maximum point. The diagrammatic representation of the velocity and acceleration at the highest point A is shown below:

3. In projectile motion, the value of the vertical component of the velocity becomes zero at the highest point because acceleration was acting on it in the opposite direction till it reaches the maximum height.

4. The value of the horizontal component of the velocity remains constant throughout the projectile motion.

Hence, the statement is false because the acceleration and velocity of a projectile in a plane to plane projectile motion are perpendicular to each other only at the maximum height of the trajectory.