If there were no air resistance,at what velocity would a drop of rain fall from a cloud 500m high?
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5000
To determine the velocity at which a drop of rain would fall from a cloud with no air resistance, you can apply the principles of free fall motion. The velocity can be found using the equations of motion.
The key equation for this scenario is the one that relates the distance fallen to the initial velocity, time, and acceleration due to gravity. The equation is:
\(s = ut + \dfrac{1}{2}gt^2\)
Where:
- \(s\) is the distance fallen (500m in this case)
- \(u\) is the initial velocity (which we need to find)
- \(g\) is the acceleration due to gravity (approximately 9.8 m/s²)
- \(t\) is the time
Since the raindrop is falling vertically downwards, its initial velocity is zero. Therefore, the equation becomes:
\(s = \dfrac{1}{2}gt^2\)
To find the time it takes for the raindrop to fall from the cloud to the ground, we can use another equation:
\(s = ut + \dfrac{1}{2}gt^2\)
Where:
- \(s\) is the distance fallen (500m)
- \(u\) is the initial velocity (which is zero)
- \(g\) is the acceleration due to gravity (approximately 9.8 m/s²)
- \(t\) is the time
Rearranging the equation, we get:
\(500 = \dfrac{1}{2}(9.8)t^2\)
Simplifying further:
\(t^2 = \dfrac{500 \times 2}{9.8}\)
\(t^2 = 102.04\)
Taking the square root of both sides:
\(t = \sqrt{102.04}\)
\(t \approx 10.1\) (rounded to one decimal place)
Now that we have the time it takes to fall, we can find the velocity using the equation:
\(v = u + gt\)
Substituting the known values:
\(v = 0 + (9.8 \times 10.1)\)
\(v = 99.98\) m/s (rounded to two decimal places)
Therefore, if there were no air resistance and the drop of rain fell from a cloud 500m high, it would reach a velocity of approximately 99.98 m/s before hitting the ground.