a stone is dropped from the rooftop of a building 60.0 m high.how many seconds does the stone take reach the ground?

Solve

H = (1/2) g t^2 for the time, t.

t = sqrt(2H/g)

H = 60 m
g = 9.8 m/s^2
t = ?

48.02

To find out how many seconds it takes for the stone to reach the ground, we can use the equation of motion for free fall:

š‘‘ = (1/2)š‘”š‘”Ā²

where:
š‘‘ = distance or height (60.0 m in this case)
š‘” = acceleration due to gravity (approximately 9.8 m/sĀ²)
š‘” = time taken

We can rearrange the equation to solve for š‘”:

2š‘‘ = š‘”š‘”Ā²

š‘”Ā² = (2š‘‘) / š‘”

š‘” = āˆš((2š‘‘) / š‘”)

Substituting the values:

š‘” = āˆš((2 * 60.0) / 9.8)

Simplifying:

š‘” = āˆš(120.0 / 9.8)

š‘” = āˆš12.24

š‘” ā‰ˆ 3.49 seconds (rounded to 2 decimal places)

Therefore, the stone takes approximately 3.49 seconds to reach the ground.

To determine how many seconds it takes for the stone to reach the ground, we can use the equation of motion for objects in free fall.

The equation is:

h = (1/2) * g * t^2

Where:
h = height (in this case, the height of the building; 60.0 m)
g = acceleration due to gravity (approximately 9.8 m/sĀ²)
t = time taken (what we want to find)

Rearranging the equation to solve for t:

t^2 = (2 * h) / g

Taking the square root of both sides:

t = āˆš[(2 * h) / g]

Let's substitute the given values into the equation and calculate the time:

t = āˆš[(2 * 60.0 m) / 9.8 m/sĀ²]

t = āˆš[(120 m) / 9.8 m/sĀ²]

t = āˆš(12.24 sĀ²)

t ā‰ˆ 3.50 s

Therefore, the stone takes approximately 3.50 seconds to reach the ground.