Question
What is the formula to calculate the time it takes for a model rocket launched vertically upward with an initial velocity of 120m/s to reach its maximum height?
Answers
GPT-4o mini
To calculate the time it takes for a model rocket launched vertically upwards with an initial velocity to reach its maximum height, you can use the following kinematic equation:
\[
v_f = v_i + a \cdot t
\]
Where:
- \( v_f \) is the final velocity (0 m/s at maximum height),
- \( v_i \) is the initial velocity (120 m/s in this case),
- \( a \) is the acceleration (which will be \(-9.81 \, \text{m/s}^2\) due to gravity),
- \( t \) is the time in seconds.
At maximum height, the final velocity \( v_f \) is 0 m/s. We can rearrange the equation to solve for \( t \):
\[
0 = 120\, \text{m/s} - 9.81\, \text{m/s}^2 \cdot t
\]
Now, rearranging gives us:
\[
9.81\, \text{m/s}^2 \cdot t = 120\, \text{m/s}
\]
Dividing both sides by \( 9.81\, \text{m/s}^2 \):
\[
t = \frac{120\, \text{m/s}}{9.81\, \text{m/s}^2} \approx 12.24\, \text{s}
\]
Therefore, the time it takes to reach maximum height is approximately **12.24 seconds**.
\[
v_f = v_i + a \cdot t
\]
Where:
- \( v_f \) is the final velocity (0 m/s at maximum height),
- \( v_i \) is the initial velocity (120 m/s in this case),
- \( a \) is the acceleration (which will be \(-9.81 \, \text{m/s}^2\) due to gravity),
- \( t \) is the time in seconds.
At maximum height, the final velocity \( v_f \) is 0 m/s. We can rearrange the equation to solve for \( t \):
\[
0 = 120\, \text{m/s} - 9.81\, \text{m/s}^2 \cdot t
\]
Now, rearranging gives us:
\[
9.81\, \text{m/s}^2 \cdot t = 120\, \text{m/s}
\]
Dividing both sides by \( 9.81\, \text{m/s}^2 \):
\[
t = \frac{120\, \text{m/s}}{9.81\, \text{m/s}^2} \approx 12.24\, \text{s}
\]
Therefore, the time it takes to reach maximum height is approximately **12.24 seconds**.