A person drops a ball from a window, 20 meters above the ground. The height of the ball (meters) above the ground after the time (seconds) is described by the formula h = 20 - 5t ^ 2. Calculate the time it takes for the ball to hit the ground.
To calculate the time it takes for the ball to hit the ground, we need to find the value of 't' when the height is 0. In the given formula, the height (h) is measured in meters and the time (t) is measured in seconds.
The formula for the height of the ball is: h = 20 - 5t^2
To find the time it takes for the ball to hit the ground (when h = 0), we can set the formula equal to zero and solve for 't':
0 = 20 - 5t^2
To solve this equation, we need to isolate the 't' term.
First, subtract 20 from both sides of the equation:
-20 = -5t^2
Next, divide both sides of the equation by -5 to isolate the 't^2' term:
4 = t^2
Now, take the square root of both sides of the equation:
√4 = √t^2
Simplifying, we get:
2 = t
Therefore, the time it takes for the ball to hit the ground is 2 seconds.
0 = 20 - 5 t^2
t^2 = 4
t = 2