a ball is dropped from the roof of a building. it takes 10 seconds to reach the ground. find the height of the building.(g=9.8/s square)
490.5
To find the height of the building, we can use the equation of motion for an object in free fall:
h = (1/2)gt^2
Where:
h = height of the building
g = acceleration due to gravity (9.8 m/s^2)
t = time taken to fall (10 seconds)
Let's substitute the values into the equation and solve for h:
h = (1/2)(9.8 m/s^2)(10 s)^2
First, calculate (10 s)^2:
h = (1/2)(9.8 m/s^2)(100 s^2)
Next, multiply 9.8 m/s^2 by 100 s^2:
h = 1/2 (980 m^2/s^2)
Lastly, divide by 2 to find the height:
h = 490 m
Therefore, the height of the building is 490 meters.
To find the height of the building, we can use the formula for the distance traveled by an object in free fall:
d = (1/2) * g * t^2
Where:
d is the distance traveled (in meters)
g is the acceleration due to gravity (in meters per second squared)
t is the time taken (in seconds)
In this case, we are given that the time taken (t) is 10 seconds and the acceleration due to gravity (g) is 9.8 m/s^2. We need to find the value of d, which is the height of the building.
Plugging in the values into the formula, we have:
d = (1/2) * 9.8 * (10^2)
= (1/2) * 9.8 * 100
= 4.9 * 100
= 490 meters
Therefore, the height of the building is 490 meters.