Question

suppose lemming a runs off the edge of the cliff at 2 m/s and lemming b runs off the edge at 1 m/s. which will hit the ground first? a both at the same time

Explanation:

Step1: Analyze vertical motion

The vertical - motion of both lemmings is a free - fall motion. The initial vertical velocity of both lemmings is \(v_{0y}=0\ m/s\), and the acceleration due to gravity \(g\) acts vertically downwards. The vertical displacement \(y\) for both lemmings is the same (height of the cliff). The equation for vertical displacement in free - fall is \(y = v_{0y}t+\frac{1}{2}gt^{2}\), with \(v_{0y} = 0\ m/s\), so \(y=\frac{1}{2}gt^{2}\), and \(t=\sqrt{\frac{2y}{g}}\).

Step2: Consider horizontal motion

The horizontal velocities of the lemmings (\(v_{A}=2\ m/s\) and \(v_{B}=1\ m/s\)) do not affect the time of fall. Horizontal and vertical motions are independent in projectile motion.

Answer:

Both at the same time