A ball is thrown from a height of 151 feet with an initial downward velocity of 15 ft/s. The ball's height h (in feet) after t seconds is given by the following
h = 151-15t-16t^2
How long after the ball is thrown does it hit the ground?
To find out when the ball hits the ground, we need to find the time at which the height h is equal to 0.
So we set h = 0:
0 = 151 - 15t - 16t^2
Rearranging the equation:
16t^2 + 15t - 151 = 0
Now we can solve this quadratic equation using the quadratic formula:
t = (-15 ± √(15^2 - 4(16)(-151))) / (2(16))
t = (-15 ± √(225 + 9672)) / 32
t = (-15 ± √9897) / 32
Since we're looking for the time after which the ball hits the ground, we only consider the positive value of t:
t ≈ 3.5 seconds
Therefore, the ball hits the ground approximately 3.5 seconds after it is thrown.