The building is 15m tall. A ball was dropped from the top of the building. How long does it take for the ball to hit the ground?
4.9t^2 = 15
t^2 = 15/4.9
t = √(15/4.9) = 1.75 sec
To find out how long it takes for the ball to hit the ground, we can use the formula:
t = √(2h/g)
Where:
- t is the time taken for the ball to hit the ground,
- h is the height of the building, and
- g is the acceleration due to gravity.
We are given that the height of the building is 15m. So, h = 15m.
The acceleration due to gravity on Earth is approximately 9.8 m/s². So, g = 9.8 m/s².
Now, let's substitute the values into the formula to calculate the time taken (t):
t = √(2 * h / g)
t = √(2 * 15m / 9.8 m/s²)
t = √(30m / 9.8 m/s²)
t = √3.06 s²
t ≈ 1.75 seconds
Therefore, it takes approximately 1.75 seconds for the ball to hit the ground.
To find out how long it takes for the ball to hit the ground, we can use a formula related to freely falling objects. The formula we can use is:
\[d = \frac{1}{2} \times g \times t^2\]
where:
- \(d\) is the distance traveled (in this case, the height of the building, which is 15m),
- \(g\) is the acceleration due to gravity (which is approximately 9.8 m/s^2), and
- \(t\) is the time.
Since we want to find the time it takes for the ball to hit the ground, we need to rearrange the formula to solve for \(t\).
Rearranging the formula, we have:
\[t = \sqrt{\frac{2d}{g}}\]
Substituting the given values, we have:
\[t = \sqrt{\frac{2 \times 15}{9.8}}\]
Calculating this, we get:
\[t \approx 1.75\ \text{s}\]
Therefore, it takes approximately 1.75 seconds for the ball to hit the ground.