A ball was dropped off a cliff and took 3.09 s to fall to the water below. Neglecting air resistance, how far (in meters) did it fall? (How far is it down to the water?)
To calculate the distance the ball fell, we can use the equation of motion for free fall:
d = (1/2) * g * t^2
Where:
- d is the distance the ball falls (what we need to find)
- g is the acceleration due to gravity (approximately 9.8 m/s^2 near the Earth's surface)
- t is the time it takes for the ball to fall (given as 3.09 s)
Plugging in the values into the equation, we get:
d = (1/2) * 9.8 * (3.09)^2
Simplifying the equation, we have:
d = 4.9 * (3.09)^2
Now, we can calculate the distance:
d ≈ 4.9 * 9.5281
d ≈ 46.68 meters
Therefore, the ball fell approximately 46.68 meters.
To calculate the distance the ball fell, we can use the formula for the distance traveled by a falling object:
d = (1/2) * g * t^2
Where:
d = distance
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
Plugging in the given values:
d = (1/2) * 9.8 m/s^2 * (3.09 s)^2
Simplifying the equation:
d = 4.9 m/s^2 * 9.54 s^2
d = 4.9 m/s^2 * 9.54 s^2 = 144.0786 m
Therefore, the ball fell approximately 144.08 meters down to the water.