Question

Use the table of data for two falling rocks to answer the 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)
Responses

1.6 seconds
1.6 seconds

4.0 seconds
4.0 seconds

0.4 second
0.4 second

40 seconds

Answer 1

To solve this problem, we can use the kinematic equations for free fall under the influence of gravity, assuming no air resistance. The equation for the distance fallen due to gravity is:

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

where:
- \( d \) is the distance fallen (height of fall in meters),
- \( g \) is the acceleration due to gravity (approximately 9.8 m/s²),
- \( t \) is the time in seconds.

We know from the data that both rocks are dropped from the same height (78.4 m). We can use the time it takes for Rock 1 to fall to find the acceleration due to gravity and check if it matches with Rock 2.

For Rock 1:
\[ 78.4 = \frac{1}{2} (9.8) (4.0)^2 \]

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

So, the calculations confirm that Rock 1's time of fall is accurate.

Now, we can apply the same calculations to Rock 2. Using the same height of 78.4 m and solving for time \( t \):

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

Solving for \( t \):
\[ 78.4 = 4.9 t^2 \]
\[ t^2 = \frac{78.4}{4.9} \]
\[ t^2 = 16 \]
\[ t = 4.0 \, \text{s} \]

Thus, Rock 2 will also take **4.0 seconds** to fall.

So, the answer is:

**4.0 seconds**.