Question
A rock falls off a cliff and hits the ground after three seconds. The rock's velocity is 29.4 m/s when it hits the ground.
What is its acceleration of the rock in the downward direction?
A.0.31 m/s2
B. 3 m/s2
C. 9.8 m/s2
D. 88.2 m/s2
What is its acceleration of the rock in the downward direction?
A.0.31 m/s2
B. 3 m/s2
C. 9.8 m/s2
D. 88.2 m/s2
Answers
GPT-4o mini
To solve the problem, we can use the information given about the rock's fall:
1. The rock falls for a total time of 3 seconds.
2. Its final velocity just before hitting the ground is 29.4 m/s.
Using the equation of motion relating final velocity (\(v\)), initial velocity (\(u\)), acceleration (\(a\)), and time (\(t\)):
\[
v = u + at
\]
Assuming the rock starts from rest, the initial velocity \(u = 0\). Thus, the equation simplifies to:
\[
v = at
\]
Substituting the values we have:
\[
29.4 \, \text{m/s} = a \cdot 3 \, \text{s}
\]
To solve for \(a\), divide both sides by 3 seconds:
\[
a = \frac{29.4 \, \text{m/s}}{3 \, \text{s}} = 9.8 \, \text{m/s}^2
\]
Thus, the acceleration of the rock in the downward direction is:
**C. 9.8 m/s²**
1. The rock falls for a total time of 3 seconds.
2. Its final velocity just before hitting the ground is 29.4 m/s.
Using the equation of motion relating final velocity (\(v\)), initial velocity (\(u\)), acceleration (\(a\)), and time (\(t\)):
\[
v = u + at
\]
Assuming the rock starts from rest, the initial velocity \(u = 0\). Thus, the equation simplifies to:
\[
v = at
\]
Substituting the values we have:
\[
29.4 \, \text{m/s} = a \cdot 3 \, \text{s}
\]
To solve for \(a\), divide both sides by 3 seconds:
\[
a = \frac{29.4 \, \text{m/s}}{3 \, \text{s}} = 9.8 \, \text{m/s}^2
\]
Thus, the acceleration of the rock in the downward direction is:
**C. 9.8 m/s²**