Final answer:
To find the time interval for a ball thrown downward from a height to hit the ground, we use a kinematic equation that accounts for initial speed and acceleration due to gravity. By substituting known values into the quadratic equation and solving for time, we determine the time interval at which the ball strikes the ground.
Step-by-step explanation:
To determine the time interval it takes for a ball to strike the ground after being thrown downward with an initial speed from a certain height, we employ the kinematic equations for uniformly accelerated motion. The equation we use in this scenario, considering the acceleration due to gravity (g = 9.81 m/s2) and ignoring air resistance, is:
h = v0t + ½gt2
Where:
- h is the initial height from which the ball is thrown (30.1 meters)
- v0 is the initial velocity of the ball (8.85 m/s downward)
- g is the acceleration due to gravity (9.81 m/s2, taken as positive in downward direction)
- t is the time in seconds
Plugging in the known values, we get:
30.1 = 8.85t + ½(9.81)t2
Which simplifies to:
0 = ½(9.81)t2 + 8.85t - 30.1
This is a quadratic equation in the standard form at2 + bt + c = 0, where a is 4.905 (half of the acceleration due to gravity), b is the initial velocity, and c is the negative of the initial height. Using the quadratic formula, t = (-b ± √(b2 - 4ac)) / (2a), we can solve for t to find the time intervals at which the ball hits the ground.
The relevant calculation gives us two solutions, but we discard the negative time and take the positive solution as the physical answer for t.