level 4 - multi - step application\n2. a carpenter tosses a tool horizontally from a 7.8 m high roof at a…

Explanation:

Step1: Analyze vertical motion

The vertical motion of the tool is a free - fall motion. The initial vertical velocity (v_{0y}=0\ m/s), the vertical displacement (y - y_0=- 7.8\ m) (taking downwards as negative), and the acceleration (a = g=-9.8\ m/s^{2}). Use the equation (y - y_0=v_{0y}t+\frac{1}{2}at^{2}). Substituting the values, we get (-7.8 = 0\times t+\frac{1}{2}\times(-9.8)t^{2}).

Step2: Solve for time (t)

From (-7.8=\frac{-9.8}{2}t^{2}), we can rewrite it as (t^{2}=\frac{7.8\times2}{9.8}). Then (t=\sqrt{\frac{15.6}{9.8}}\approx1.26\ s).

Step3: Find final vertical velocity

Use the equation (v_y = v_{0y}+at). Since (v_{0y} = 0\ m/s), (a=-9.8\ m/s^{2}) and (t\approx1.26\ s), then (v_y=0+(-9.8)\times1.26=- 12.35\ m/s) (the negative sign indicates the direction is downwards).

Answer:

a. The time it takes to reach the ground is approximately (1.26\ s). b. The final vertical velocity just before hitting the ground is approximately (-12.35\ m/s).