Question

6 formula 1 point
a ball is dropped from rest on earth. the ball falls to the ground in 1.5 seconds. how far must it have fallen during this time?
answer

Explanation:

Step1: Identify the formula

For an object in free fall (dropped from rest, so initial velocity \( u = 0 \)), the distance \( s \) fallen is given by the formula \( s=\frac{1}{2}gt^{2} \), where \( g = 9.8\ m/s^{2} \) (acceleration due to gravity on Earth) and \( t \) is the time.

Step2: Substitute the values

We know \( t = 1.5\ s \) and \( g = 9.8\ m/s^{2} \). Substitute these into the formula:
\( s=\frac{1}{2}\times9.8\times(1.5)^{2} \)
First, calculate \( (1.5)^{2}=2.25 \). Then, \( \frac{1}{2}\times9.8 = 4.9 \). Now multiply \( 4.9\times2.25 \).
\( 4.9\times2.25 = 11.025 \) meters.

Answer:

\( 11.025\) meters (or approximately \( 11.0\) meters or \( 11\) meters depending on significant figures, but the precise calculation gives \( 11.025\) m)