Question
What is the time it takes for a missile to reach the ground if it is released horizontally from a 300 m high cliff?
Answers
GPT-4o mini
To determine the time it takes for a missile to reach the ground when released horizontally from a height, we can use the physics of free fall. The horizontal motion does not affect the time it takes to fall vertically, so we can focus solely on the vertical motion.
The relevant formula for the distance fallen under the influence of gravity is:
\[
d = \frac{1}{2}gt^2
\]
where:
- \( d \) is the height from which the missile is dropped (300 m in this case),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.
We can rearrange this formula to solve for \( t \):
\[
t^2 = \frac{2d}{g}
\]
\[
t = \sqrt{\frac{2d}{g}}
\]
Now plug in the values:
\[
d = 300 \, \text{m}, \quad g = 9.81 \, \text{m/s}^2
\]
Calculating \( t \):
\[
t = \sqrt{\frac{2 \times 300}{9.81}} = \sqrt{\frac{600}{9.81}} \approx \sqrt{61.13} \approx 7.81 \, \text{s}
\]
Therefore, it takes approximately **7.81 seconds** for the missile to reach the ground.
The relevant formula for the distance fallen under the influence of gravity is:
\[
d = \frac{1}{2}gt^2
\]
where:
- \( d \) is the height from which the missile is dropped (300 m in this case),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( t \) is the time in seconds.
We can rearrange this formula to solve for \( t \):
\[
t^2 = \frac{2d}{g}
\]
\[
t = \sqrt{\frac{2d}{g}}
\]
Now plug in the values:
\[
d = 300 \, \text{m}, \quad g = 9.81 \, \text{m/s}^2
\]
Calculating \( t \):
\[
t = \sqrt{\frac{2 \times 300}{9.81}} = \sqrt{\frac{600}{9.81}} \approx \sqrt{61.13} \approx 7.81 \, \text{s}
\]
Therefore, it takes approximately **7.81 seconds** for the missile to reach the ground.