Question

a ball rolls horizontally off a table 1.5 m high and falls to the ground. which statement correctly describes its motion as it falls to the ground? a its horizontal and its vertical speed increase. b its horizontal and its vertical speed do not change. c its horizontal speed increases and its vertical speed does not change. d its horizontal speed does not change and its vertical speed increases.

Explanation:

Step1: Analyze horizontal motion

In projectile motion (assuming no air resistance), the horizontal velocity \(v_x\) remains constant because there is no horizontal acceleration (\(a_x = 0\)). The formula for horizontal velocity is \(v_x=\frac{\Delta x}{t}\), and since \(a_x = F_x/m\) and \(F_x = 0\) (no horizontal force), \(v_x\) doesn't change.

Step2: Analyze vertical motion

The vertical motion is under the influence of gravity. The initial vertical velocity \(v_{y0}=0\) (ball rolls horizontally off the table). The acceleration \(a_y=-g=- 9.8\space m/s^{2}\) (down - ward). Using the kinematic equation \(v_y = v_{y0}+a_yt\), with \(v_{y0} = 0\), we get \(v_y=-gt\). As time \(t\) increases (while the ball is falling), the magnitude of the vertical velocity \(|v_y|\) increases.

Answer:

D. Its horizontal speed does not change and its vertical speed increases.