To determine the time it takes for the ball to hit the ground, we can use the equations of motion. In this case, we will use the equation:
h = v0 * t + (1/2) * g * t^2
Where:
h = initial height (1 ft)
v0 = initial velocity (15 m/s)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time
We want to find the time it takes for the ball to hit the ground, so we can set h equal to zero:
0 = v0 * t + (1/2) * g * t^2
Rearranging the equation, we get:
(1/2) * g * t^2 + v0 * t = 0
Now, we can solve this quadratic equation for t using the quadratic formula:
t = (-v0 ± √(v0^2 - 4*(1/2)*g*0)) / 2*(1/2)*g
Simplifying this equation further, we get:
t = (-v0 ± √(v0^2 - 2 * g * 0)) / g
Since we want the time it takes for the ball to hit the ground, the positive value of t is the solution we are interested in. Therefore, we use the positive sign before the square root:
t = (-v0 + √(v0^2 - 2 * g * 0)) / g
Substituting the given values:
t = (-15 + √(15^2 - 2 * 9.8 * 0)) / 9.8
Simplifying further:
t = (-15 + √(225 - 0)) / 9.8
t = (-15 + √225) / 9.8
t = (-15 + 15) / 9.8
t = 0 / 9.8
t = 0
Therefore, the time it takes for the ball to hit the ground is 0 seconds.