Question

Match the entries of the left columns with the entries of the right columns:

Column 1	Column 2
For a plane to plane projectile motion	Acceleration is constant
For a particle projected horizontal from a height	Horizontal component of velocity remains constant.
For a particle projected upwards( angle not equal to ${90}^{\circ }$from horizontal from a height)	Velocity is changing in magnitude as well as direction.
For a particle projected in vertically upward direction from ground	Acceleration is changing.

Answer 1

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 $\left(g\right)$. Hence, the direction of acceleration will be downwards.

Part A:

The diagrammatic representation for a plane to plane projectile motion is given below:

1. For a plane to plane projectile motion, acceleration remains constant, the horizontal component of velocity remains constant and velocity is changing in magnitude as well as direction.
2. The acceleration is zero in the horizontal direction and is equal to the gravity in the vertical direction
3. As the value of g remains constant throughout the projectile motion. acceleration is constant.
4. The projectile's horizontal speed is constant throughout the entire trajectory because gravity only acts downwards in the vertical direction. Hence horizontal velocity is constant.
5. The magnitude as well as the direction of the velocity keeps changing throughout the projectile motion.

Thus, A - I, II, III

Part B:

The diagrammatic representation of a particle projected horizontally from a height is given below:

1. For a particle projected horizontally from a height, acceleration remains constant, the horizontal component of velocity remains constant and velocity is changing in magnitude as well as direction.
2. Acceleration is constant for a particle projected horizontally from height because when the projectile is in air and air resistance is neglected, the only force acting on it is the gravitational force.
3. The horizontal component of velocity remains constant because there is no acceleration in that direction.
4. For a particle from height, its velocity is changing in magnitude as well as direction, as it is always tangential to the path and the path curves.

Thus, B - I, II, III

Part C:

1. When a particle is projected upwards it follows a plane to plane projectile motion as explained in part A.
2. For a particle projected upwards at an angle not equal to ${90}^{\circ }$horizontal from a height, acceleration remains constant, the horizontal component of velocity remains constant and velocity is changing in magnitude as well as direction.
3. At the highest point, the velocity is equal to zero, its acceleration becomes constant.
4. The horizontal component of velocity remains constant because the force of gravity does not affect the horizontal component of motion.
5. The magnitude as well as the direction of the velocity keeps changing throughout the projectile motion.

Thus, C - I, II, III

Part D:

The diagrammatic representation of a particle projected in a vertically upward direction from the ground is given below:

1. For a particle projected in a vertically upward direction from the ground, acceleration remains constant and velocity is changing in magnitude as well as direction.
2. Acceleration is constant for a particle projected in an upwards direction from the ground.
3. Velocity is changing in magnitude as well as direction for a particle projected vertically upwards as it is always tangential to the path and the path curves.

Thus, D - I, III