Question

The velocity of a projectile equals to its initial velocity added to

• A. a constant horizontal velocity
• B. a constant vertical velocity
• C. a continuously increasing horizontal velocity
• D. a continuously increasing downward velocity

Answer 1

The correct option is D

a continuously increasing downward velocity

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.

Explanation for correct option:

Option D:

1. When the projectile is launched from a height horizontally, the vertical motion is one of constant downward acceleration.
2. The horizontal component remains constant throughout the motion.
3. Therefore, the velocity of a projectile equals its initial velocity when added to a constantly increasing downward velocity.

Explanation for incorrect options:

Option A:

1. The formula to calculate the velocity vector is $u=\sqrt{{\left(u_x\right)}^2+{\left(u_y\right)}^2}$ at any instance.
2. A constant horizontal velocity $u_x$ does not result in an increase in the overall velocity of the projectile.
3. Therefore, the velocity of a projectile is not equal to its initial velocity when added to a constant horizontal velocity.

Option B:

1. A projectile motion does not have a constant vertical velocity because gravity is acting on it in a downward direction throughout the motion.
2. Therefore, the velocity of a projectile cannot be added to a constant vertical velocity.

Option C:

1. A projectile motion has a constant horizontal velocity.
2. Therefore, the velocity of a projectile cannot be added to a continuously increasing horizontal velocity.

Hence, the correct option is option D.