Question

Answer the following questions for projectile motion on level ground assuming negligible air resistance (the initial angle being neither\(0^\circ \)nor\(90^\circ \)):

(a) Is the acceleration ever zero?

(b) Is the acceleration ever in the same direction as a component of velocity?

(c) Is the acceleration ever opposite in direction to a component of velocity?

Short answer

(a) The acceleration of the projectile is never zero.

(b) When the particle starts to descend, the direction of acceleration is the same as the direction of the component of the velocity.

(c) When the projectile ascends, the direction of acceleration is in the opposite direction of the component of the velocity.

Step-by-step solution

Projectile motion

Projectile motion is the motion of an item projected at an angle that is only affected by gravity's acceleration.The object is known as a projectile, and it follows a trajectory, which is a parabolic path.

(a) Zero acceleration

When a projectile is projected at some angle from horizontal, the acceleration due to gravity continuously alters its velocity.

Hence, the acceleration of a projectile is always finite and non-zero.

(b) Acceleration in the same direction as a component of velocity

The acceleration due to gravity acts continuously on a projectile and is always directed downwards towards the center of Earth, and the projectile travels in a parabolic path represented as,

From the diagram, the velocity of the projectile as it travels from \(A\) to \(B\) is directed downwards along the tangent to its path. As the projectile traces the path \(AB\), its vertical component of velocity is always directed downwards along the direction of acceleration due to gravity.

Hence, when the particle starts to descend, the direction of acceleration is the same as the direction of the component of the velocity.

(c) Acceleration in the opposite direction as a component of velocity

The acceleration due to gravity acts continuously on a projectile and is always directed towards downwards the center of Earth, and the projectile travels in a parabolic path represented as,

From the diagram, the velocity of the projectile as it travels from \(O\) to \(A\) is directed upwards along the tangent to its path. As the projectile traces the path \(OA\), its vertical component of velocity is always directed upwards opposite in the direction of acceleration due to gravity.

Hence, when the projectile ascends, the direction of acceleration is in the opposite direction of the component of the velocity.