Ground to Ground Projectile: Practice Problem & Solution
Assertion (A): Two stones are simultaneously projected from level ground from same point with same speeds but different angles with horizontal. Both stones move in same vertical plane. Then the two stones may collide in mid air. Reason (R): For two stones projected simultaneously from same point with same speed at different angles with horizontal, their trajectories must intersect at some point except projection point.
Solution Explained:
To solve this problem, we apply the core principles of Ground to Ground Projectile. Understanding the underlying formula is key to arriving at the correct answer below:
For collision, the projectiles must be at the same position at the same time. If launched simultaneously from the same point, their x-positions at time \(t\) are \(x_1 = u \cos\theta_1 t\) and \(x_2 = u \cos\theta_2 t\). For \(x_1 = x_2\) at \(t > 0\), \(cos\theta_1 = \cos\theta_2\), which means \(theta_1 = \theta_2\), contradicting 'different angles'. Hence, they cannot collide. So (A) is false. Trajectories \(y = x \tan\theta - \frac{g x^2}{2 u^2 \cos^2\theta}\) do intersect for \(0 < \theta_1, \theta_2 < 90^\circ\), but if extreme angles (\(0^\circ\) or \(90^\circ\)) are included, trajectories may not intersect beyond the origin. Thus, (R) is false in a general sense.
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