Question

A worker on the roof of a 3rd story building drops a tool from 30 feet. Which is a step in solving for how long it would take for the tool to hit the ground?

Answer 1

To solve for the time a tool takes to hit the ground from a 30-foot drop, convert the height to meters and use the kinematic equation for vertical motion, setting up the equation with gravity's acceleration and solving for time.

Step-by-step explanation:

Understanding Time of Descent for a Falling Object

To calculate the time it takes for a tool to hit the ground from a 30-foot drop, we can use the kinematic equation for vertical motion without air resistance:

• y = y0 + v0t + ½at²

In this case, the initial position y0 is the height from which the tool is dropped (30 feet), the initial velocity v0 is 0 m/s (since the tool is dropped and not thrown), and a is the acceleration due to gravity, which is approximately -9.8 m/s² (the negative sign indicates that gravity is pulling the object downward).

Converting the height from feet to meters will allow us to use the metric system, which is standard in physics calculations. We can start by setting up the equation:

• y = ½(-9.8)t²

From there, we solve for t to find the time in seconds it takes for the tool to reach the ground. This step involves algebraic manipulation to isolate t and finding its numerical value.