Question
What is the maximum height achieved if a 0.800 kg mass is thrown straight upward with an initial speed of 20.0 m/s?
Answers
GPT-4o mini
To find the maximum height achieved by the mass, we can use the following kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:
\[
v^2 = u^2 + 2a s
\]
Where:
- \( v \) is the final velocity (0 m/s at the maximum height),
- \( u \) is the initial velocity (20.0 m/s),
- \( a \) is the acceleration (which will be \(-g = -9.81 \, \text{m/s}^2\) due to gravity),
- \( s \) is the displacement (the maximum height we want to find).
Rearranging the equation to solve for \( s \):
\[
0 = (20.0)^2 + 2(-9.81)s
\]
\[
0 = 400 - 19.62s
\]
\[
19.62s = 400
\]
\[
s = \frac{400}{19.62} \approx 20.39 \, \text{m}
\]
Therefore, the maximum height achieved is approximately **20.4 meters**.
\[
v^2 = u^2 + 2a s
\]
Where:
- \( v \) is the final velocity (0 m/s at the maximum height),
- \( u \) is the initial velocity (20.0 m/s),
- \( a \) is the acceleration (which will be \(-g = -9.81 \, \text{m/s}^2\) due to gravity),
- \( s \) is the displacement (the maximum height we want to find).
Rearranging the equation to solve for \( s \):
\[
0 = (20.0)^2 + 2(-9.81)s
\]
\[
0 = 400 - 19.62s
\]
\[
19.62s = 400
\]
\[
s = \frac{400}{19.62} \approx 20.39 \, \text{m}
\]
Therefore, the maximum height achieved is approximately **20.4 meters**.