Question

carly drops a golf ball from her third - floor window and records the time it takes for the ball to hit the ground. she knows that the distance, d, that a dropped object travels can be calculated using the formula ( d=\frac{1}{2}gt^{2} ), where g is a constant representing the force of gravity and t is the time spent falling.
carly uses seconds (s) to measure time, and she plans to determine the height of her window in meters (m). what units should carly use for g?
s/m m/s ( s/m^{2} ) ( m/s^{2} )

Explanation:

Step1: Analyze the formula units

We know that \(d\) has units of meters (\(m\)) and \(t\) has units of seconds (\(s\)). The formula is \(d=\frac{1}{2}gt^{2}\).

Step2: Solve for the units of \(g\)

From \(d = gt^{2}\) (ignoring the \(\frac{1}{2}\) as it is dimensionless), we can express \(g=\frac{d}{t^{2}}\). Substituting the units: \(g\) has units \(\frac{m}{s^{2}}\).

Answer:

\(m/s^{2}\)