If we ignore the effects of air resistance and only consider the influence of gravity, the distance a ball travels when dropped from rest depends on the height from which it was dropped. The distance traveled can be calculated using the equations of motion under constant acceleration.
The formula to calculate the distance traveled (d) by an object under free fall is given by:
d = 1/2 * g * t^2
Where: g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth) t is the time of fall
To calculate the time of fall, we can use the following formula:
t = sqrt(2h / g)
Where: h is the initial height from which the ball is dropped
For example, if the ball is dropped from a height of 10 meters:
t = sqrt(2 * 10 / 9.8) = 1.43 seconds (rounded to two decimal places)
Now we can calculate the distance traveled:
d = 1/2 * 9.8 * (1.43^2) = 10.24 meters (rounded to two decimal places)
Therefore, if we ignore air resistance, a ball dropped from rest from a height of 10 meters would travel approximately 10.24 meters downward.