Question

Rock 1 Rock 2

Mass (kg)
2.5
25
Height of Fall (m)
78.4
78.4
Time to Fall (s)
4.0
?
Based on this data, how many seconds will it take rock 2 to fall?
(1 point)
• 40 seconds
• 4.0 seconds
• 0.4 second
• 1.6 seconds

Answer 1

To determine how long it will take for Rock 2 to fall, we can use the equation for the time of free fall, which is derived from the physics of falling objects under gravity:

\[
d = \frac{1}{2} g t^2
\]

Where:
- \(d\) is the distance fallen (height) in meters,
- \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\)),
- \(t\) is the time in seconds.

We are given that Rock 1 (mass 2.5 kg) falls from a height of 78.4 meters, taking 4.0 seconds to fall. Let's verify this with the formula:

\[
78.4 = \frac{1}{2} \cdot 9.8 \cdot (4.0)^2
\]

Calculating the right-hand side:
\[
\frac{1}{2} \cdot 9.8 \cdot 16 = 78.4
\]

This confirms that Rock 1's time to fall is correct.

Since both rocks are falling from the same height (78.4 meters) and are in free fall, the time it takes for Rock 2 (mass 25 kg) to fall will be the same as for Rock 1 because the mass of the object does not affect the time of free fall in a vacuum.

Therefore, the time for Rock 2 to fall is also 4.0 seconds.

The correct answer is:
• 4.0 seconds