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A stone thrown from the top of a building is given an initial velocity of 20.0 m/s straight upward. Determine the time in seconds at which the stone returns to the height from which it was thrown.
g = 9.8 m /
sec2
- a)3.45
- b)3.46
- c)4.52.
- d)4.08
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A stone thrown from the top of a building is given an initial velocity...
Again to reach same level from where it has been thrown it have to cover same distance downward.
For this initial velocity u = 0
s = 20.4 m
a = 9.8 m/s2 (+be because motion is in same direction).
So,
Most Upvoted Answer
A stone thrown from the top of a building is given an initial velocity...
Given:
Initial velocity, u = 20.0 m/s (upward)
Acceleration due to gravity, g = 9.8 m/s²
To find:
Time taken by the stone to return to its initial height.
Solution:
When the stone is thrown upward, its velocity decreases with time until it reaches its maximum height and then starts to fall back down due to the force of gravity.
At the maximum height, the velocity of the stone becomes zero. Let's find the time taken for the stone to reach this maximum height.
Using the equation of motion:
v = u + gt
where,
v = final velocity (when the stone reaches its maximum height)
u = initial velocity
g = acceleration due to gravity
t = time taken
At maximum height, v = 0 (since the stone momentarily stops moving)
So, 0 = 20.0 - 9.8t
=> t = 20.0/9.8
=> t = 2.04 seconds (approx)
Now, the stone starts to fall back down with an initial velocity of zero (at the maximum height) and acceleration due to gravity, g = 9.8 m/s².
To find the time taken for the stone to return to its initial height, we can use the same equation of motion:
h = ut + (1/2)gt²
where,
h = height
u = initial velocity
g = acceleration due to gravity
t = time taken
At the initial height, h = 0 (since the stone started from this height)
So, 0 = 20.0t - (1/2)9.8t²
=> 4.9t² = 20.0t
=> t(4.9t - 20.0) = 0
=> t = 0 (when the stone is thrown) or t = 20.0/4.9
=> t ≈ 4.08 seconds (when the stone returns to its initial height)
Therefore, the time taken by the stone to return to its initial height is approximately 4.08 seconds.
Answer: (d) 4.08
Initial velocity, u = 20.0 m/s (upward)
Acceleration due to gravity, g = 9.8 m/s²
To find:
Time taken by the stone to return to its initial height.
Solution:
When the stone is thrown upward, its velocity decreases with time until it reaches its maximum height and then starts to fall back down due to the force of gravity.
At the maximum height, the velocity of the stone becomes zero. Let's find the time taken for the stone to reach this maximum height.
Using the equation of motion:
v = u + gt
where,
v = final velocity (when the stone reaches its maximum height)
u = initial velocity
g = acceleration due to gravity
t = time taken
At maximum height, v = 0 (since the stone momentarily stops moving)
So, 0 = 20.0 - 9.8t
=> t = 20.0/9.8
=> t = 2.04 seconds (approx)
Now, the stone starts to fall back down with an initial velocity of zero (at the maximum height) and acceleration due to gravity, g = 9.8 m/s².
To find the time taken for the stone to return to its initial height, we can use the same equation of motion:
h = ut + (1/2)gt²
where,
h = height
u = initial velocity
g = acceleration due to gravity
t = time taken
At the initial height, h = 0 (since the stone started from this height)
So, 0 = 20.0t - (1/2)9.8t²
=> 4.9t² = 20.0t
=> t(4.9t - 20.0) = 0
=> t = 0 (when the stone is thrown) or t = 20.0/4.9
=> t ≈ 4.08 seconds (when the stone returns to its initial height)
Therefore, the time taken by the stone to return to its initial height is approximately 4.08 seconds.
Answer: (d) 4.08
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Community Answer
A stone thrown from the top of a building is given an initial velocity...
U=20m/s v=(-20 m/s) g=(-9.8m/s) t=? v=u+at -20=20-9.8t 9.8t=40 t=40/9.8=4.08 hence t = 4.08sec
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A stone thrown from the top of a building is given an initial velocity of 20.0 m/s straight upward. Determine the time in seconds at which the stone returns to the height from which it was thrown.g = 9.8 m / sec2a)3.45b)3.46c)4.52.d)4.08Correct answer is option 'D'. Can you explain this answer?
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