Path of a projected particle under gravity/uniform acceleration – Rankers Physics

Equations of Motion: Practice Problem & Solution

A particle is projected with a velocity \( \vec{v} = (3\hat{i} + 4\hat{j}) \text{ m/s} \) in the presence of uniform acceleration \( \vec{a} = (4\hat{i} - 3\hat{j}) \text{ m/s}^2 \). The path of the particle will be
Straight line
Parabolic
Circular
Elliptical

Solution Explained:

To solve this problem, we apply the core principles of Equations of Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Since the constant acceleration vector \( \vec{a} \) is not parallel or antiparallel to the initial velocity vector \( \vec{v} \) (here \( \vec{v} \cdot \vec{a} = 0 \)), the trajectory of the particle is parabolic.

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