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Raindrops fall to the ground from a cloud 1700 m above Earth's surface. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? Would it be safe to walk outside during a rainstorm?

Raindrops fall to the ground from a cloud 1700 m above Earth's surface. If they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? Would it be safe to walk outside during a rainstorm?

Grade:upto college level

3 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
Given:
Height from which raindrops fall, x = 1700 m.
Initial speed of raindrops, v0 = 0 m/s.
Acceleration due to gravity, g = 9.8 m/s2.
From the equation of kinematics, we have

232-1271_8.PNG
Where v represents the final speed of the object under consideration, a is its acceleration, v0 the initial speed and t the time for which the object is studied.
We can solve for acceleration from the above two equation by eliminating the variable .
From the second equation, the time t is given as:
t = \frac{v-v_{0}}{a}
Substitute the value in first equation

Since the rain drops falls freely, the acceleration they experience equals the acceleration due to gravity that is g. Also, under free fall, the raindrops fall with zero initial speed and it is assumed that the downward motion is considered positive.

Substitutes the value in the equation above to obtain the final velocity v as:
232-1155_9.PNG
Since the rain drops falls freely, the acceleration they experience equals the acceleration due to gravity that is g. Also, under free fall, the raindrops fall with zero initial speed and it is assumed that the downward motion is considered positive.
Substitutes the value in the equation above to obtain the final velocity v as:
232-1964_10.PNG
Rounding off to two significant figures
Rounding off to two significant figures
v = 180 m/s
Therefore the raindrops fall on ground with speed 180 m/s.
From the speed of the raindrops, with which they hit the ground, it is not safe to walk outside during the rain storm. However the effect of the impact also depends on the mass of the raindrops.
Chhoennyi R W
11 Points
6 years ago
given, height(s) = 1700m
initial velocity (u) = 0
final velocity (v) = ?
acceleration (in this case, due to gravity, g) = 9.8 m/s2
 
we know the formula, v2 = u2 + 2as
Putting in the given values, v2 = 0 + (2 x 9.8 x 1700)
                                       so, v  = sq.root (2 x 9.8 x 1700)  = 182.5 m/s.
 
Radha
15 Points
3 years ago
A spherical raindrop starting from rest falls under the influence of gravity if it gather in outer vapor at a rate promotional to it's surface and if it's initial radius is 0 show that it falls with constant acceleration g/4

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