Final answer:
The correct equation to determine the time when a tool will land on the ground is 0 = -16t^2 + 50. Solving this quadratic equation gives us the positive root t = 1.77 seconds, which is the time it will take for the tool to reach the ground.
Step-by-step explanation:
To determine at what time a tool will land on the ground given its vertical motion, we can use a physics equation that relates height (h), time (t), and acceleration due to gravity (g), assuming the only force acting on the tool is gravity. The standard form for this type of motion, where the height is zero when the tool touches the ground, is given by 0 = -16t^2 + vt + h0, where 'v' is the initial velocity and 'h0' is the initial height. In this case, since no initial velocity or height is provided, we can infer from the possible options that the correct equation is a) 0 = -16t^2 + 50.
Now, to solve for time t, we can use the basic principles of algebra to find the roots of the equation. This equation is already set equal to 0, which means it's ready for us to solve. Here, t represents the time in seconds it will take for the tool to hit the ground. Using the quadratic formula or factoring, we can solve for t by rearranging the equation to -16t^2 + 50 = 0. This yields us two roots, and since we cannot have negative time, we select the positive root as the time it takes for the tool to land on the ground. Solving this equation gives us t = 1.77 seconds.