A ball is dropped from the roof of a building. How much time does it take to reach a velocity of 15.4 m/s?
To determine the time it takes for the ball to reach a velocity of 15.4 m/s, we need to use the equation of motion that relates velocity, time, and acceleration.
The equation we'll use is:
v = u + at
Where:
- v is the final velocity (15.4 m/s),
- u is the initial velocity (in this case, 0 m/s because the ball is dropped without any initial velocity),
- a is acceleration (which we'll assume to be the acceleration due to gravity, approximately 9.8 m/s²),
- t is the time (what we're trying to find).
Given that information, we can rearrange the equation to isolate the time variable:
t = (v - u) / a
Plugging in the values:
t = (15.4 - 0) / 9.8
Using a calculator, we can simplify this equation:
t ≈ 1.57 seconds
Therefore, it takes approximately 1.57 seconds for the ball to reach a velocity of 15.4 m/s when dropped from the roof of the building.