A ball is dropped from a cliff that is 224 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S=16t^2. How many seconds (to tenths) will it take for the ball to hit the ground?
Find t when: 224 = 16 t^2
To find out how many seconds it will take for the ball to hit the ground, we need to set the distance S equal to 224 feet and solve for t in the equation S = 16t^2.
The equation given is S = 16t^2, where S represents the height of the ball at any given time t.
We know that when the ball hits the ground, its height is 0. So, we can set S = 0 and solve for t.
0 = 16t^2
Divide both sides of the equation by 16:
0/16 = (16t^2)/16
0 = t^2
Taking the square root of both sides:
√0 = √t^2
0 = t
Therefore, the ball will hit the ground at t = 0 seconds.
However, it's important to note that the formula S = 16t^2 gives the distance fallen by the ball in t seconds, starting from rest. In reality, the ball would take a fraction of a second to actually fall from the initial height. The formula assumes ideal conditions and neglects factors such as air resistance.