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It is a common observation that rain clouds can be at about 1 km altitude above the ground. If a rain drop falls from such a height freely under gravity, then what will be its speed in km h-1 (Take g = 10 m )
- a)510
- b)610
- c)710
- d)910
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
It is a common observation that rain clouds can be at about 1 km altit...
Given:
- Height of rain clouds above the ground = 1 km = 1000 m
- Acceleration due to gravity (g) = 10 m/s²
To find:
- Speed of the raindrop in km/h
Solution:
We can solve this problem using the equations of motion.
Step 1: Finding the time taken by the raindrop to fall
Using the second equation of motion:
v = u + gt
Where,
v = final velocity (which is 0 m/s as the raindrop falls freely)
u = initial velocity (which is also 0 m/s as the raindrop starts from rest)
g = acceleration due to gravity
t = time taken
0 = 0 + (10)(t)
0 = 10t
t = 0 s
The time taken by the raindrop to fall is 0 seconds.
Step 2: Converting the height and time into the same units
Since the height of the rain clouds is given in kilometers and the time is given in seconds, we need to convert them into the same units. Let's convert the height into meters.
Height of rain clouds = 1 km = 1000 m
Step 3: Finding the final velocity
Using the first equation of motion:
v = u + gt
Where,
v = final velocity
u = initial velocity (which is 0 m/s)
g = acceleration due to gravity (10 m/s²)
t = time taken (0 s)
v = 0 + (10)(0)
v = 0 m/s
The final velocity of the raindrop is 0 m/s.
Step 4: Converting the speed into km/h
Since the final velocity is given in m/s, we need to convert it into km/h.
Speed of the raindrop = 0 m/s
Speed of the raindrop = 0 × 3.6 km/h (1 m/s = 3.6 km/h)
The speed of the raindrop is 0 km/h.
Therefore, the correct answer is option 'A' (0 km/h).
- Height of rain clouds above the ground = 1 km = 1000 m
- Acceleration due to gravity (g) = 10 m/s²
To find:
- Speed of the raindrop in km/h
Solution:
We can solve this problem using the equations of motion.
Step 1: Finding the time taken by the raindrop to fall
Using the second equation of motion:
v = u + gt
Where,
v = final velocity (which is 0 m/s as the raindrop falls freely)
u = initial velocity (which is also 0 m/s as the raindrop starts from rest)
g = acceleration due to gravity
t = time taken
0 = 0 + (10)(t)
0 = 10t
t = 0 s
The time taken by the raindrop to fall is 0 seconds.
Step 2: Converting the height and time into the same units
Since the height of the rain clouds is given in kilometers and the time is given in seconds, we need to convert them into the same units. Let's convert the height into meters.
Height of rain clouds = 1 km = 1000 m
Step 3: Finding the final velocity
Using the first equation of motion:
v = u + gt
Where,
v = final velocity
u = initial velocity (which is 0 m/s)
g = acceleration due to gravity (10 m/s²)
t = time taken (0 s)
v = 0 + (10)(0)
v = 0 m/s
The final velocity of the raindrop is 0 m/s.
Step 4: Converting the speed into km/h
Since the final velocity is given in m/s, we need to convert it into km/h.
Speed of the raindrop = 0 m/s
Speed of the raindrop = 0 × 3.6 km/h (1 m/s = 3.6 km/h)
The speed of the raindrop is 0 km/h.
Therefore, the correct answer is option 'A' (0 km/h).
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Community Answer
It is a common observation that rain clouds can be at about 1 km altit...
Here, u = 0, g = 10 ms-2, h = 1 km = 1000 m
As v2 - u2 = 2gh
∴ v2 = 2gh
As v2 - u2 = 2gh
∴ v2 = 2gh
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