Question

A particle is projected at an angle \( \theta \) with the x-axis in the xy-plane with a velocity \( \mathbf{v} = 6\hat{i} - 4\hat{j} \). The velocity of the body on reaching the x-axis again is:

• A. \( 6\hat{i} - 4\hat{j} \)
• B. \( 12\hat{i} - 8\hat{j} \)
• C. \( 3\hat{i} - 2\hat{j} \)
• D. \( 3\hat{i} + 2\hat{j} \)
• E. \( 6\hat{i} + 4\hat{j} \)

Hint:

In projectile motion, the horizontal velocity remains unchanged, while the vertical velocity reverses its sign upon reaching the same level.

Answer 1

Answer: (E)

The velocity vector of the particle is given as: \[ \mathbf{v} = 6\hat{i} - 4\hat{j} \] In projectile motion: 
- The horizontal component of velocity remains constant because no horizontal force acts on the object. 
- The vertical component of velocity reverses its sign when the object returns to the same horizontal level (due to gravity). 
Thus, at the time the body reaches the x-axis again: \[ \text{New velocity} = 6\hat{i} + 4\hat{j} \]