V = 30m/1.5s = 20 m/s = Final velocity.
h = (V^2-Vo^2)/2g.
h = (400-0)/19.6 = 20.41 m.
h = (V^2-Vo^2)/2g.
h = (400-0)/19.6 = 20.41 m.
h = (1/2) * g * t^2
where:
- h is the height
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time taken to fall
Given:
- Distance traveled in the last 30.0 meters
- Time taken is 1.50 seconds
We can rearrange the equation to solve for the initial height:
h = (1/2) * g * t^2
h = (1/2) * 9.8 m/s^2 * (1.50 s)^2
h = (1/2) * 9.8 m/s^2 * 2.25 s^2
h = 1/2 * 9.8 m/s^2 * 2.25 s^2
h = 1/2 * 9.8 m/s^2 * 2.25 s^2
h = 11.025 m
Therefore, the object fell from a height of 11.025 meters above the ground.
h = v₀t + (1/2)gt²
In this case, the initial velocity is zero because the object begins its fall from rest. The acceleration due to gravity (g) is approximately 9.8 m/s². The time (t) is given as 1.50 seconds, and we are looking for the height (h).
So, we can rewrite the equation as:
h = (1/2)gt²
Substituting the given values:
h = (1/2)(9.8 m/s²)(1.50 s)²
h = (1/2)(9.8 m/s²)(2.25 s²)
h = 11.025 m
Therefore, the object fell from a height of 11.025 meters above the ground.