Relative Motion in One Dimension: Practice Problem & Solution

Solution Explained:

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

Position of B: \(y_B(t) = H - (1/2)gt^2\). Meeting at \(H/2\): \(H/2 = H - (1/2)gt^2 \Rightarrow (1/2)gt^2 = H/2 \Rightarrow t = \sqrt{H/g}\). Position of A: \(y_A(t) = v_0t - (1/2)gt^2\). At meeting: \(H/2 = v_0t - H/2 \Rightarrow H = v_0t\). Substitute \(t\): \(H = v_0 \sqrt{H/g}\). Squaring both sides gives \(H^2 = v_0^2 (H/g) \Rightarrow v_0^2 = gH\).