Assuming no air resistance, how long does it take a penny to fall if it was thrown down with an initial velocity of 5.0 m/s from the CN Tower (553 m)?
To determine how long it takes for a penny to fall from a certain height, we can use the equation for motion under constant acceleration. In this case, the acceleration is due to gravity, which is approximately 9.8 m/s². The equation we can use is:
s = ut + 0.5 * a * t²
Where:
s = distance (height) fallen
u = initial velocity
a = acceleration due to gravity (9.8 m/s²)
t = time
In this scenario, the initial velocity (u) is given as 5.0 m/s, and the height (s) is given as 553 m. We need to solve for time (t). Rearranging the equation, we get:
t = √((2s) / a)
Substituting the values for s and a into the equation:
t = √((2 * 553 m) / 9.8 m/s²)
Now, we can calculate the time it takes for the penny to fall by plugging in the values into a calculator:
t ≈ √(1126 / 9.8)
t ≈ √(115.10)
t ≈ 10.72 seconds
Therefore, assuming no air resistance, it would take approximately 10.72 seconds for the penny to fall from the CN Tower with an initial velocity of 5.0 m/s.