Answer:
To find the time interval during which the height of the ball is less than 17 feet, we need to solve the equation H = -16t^2 + 81 for t when H is less than 17.
Let's substitute H with 17 in the equation and solve for t:
17 = -16t^2 + 81
Rearranging the equation, we get:
-16t^2 = 17 - 81
-16t^2 = -64
Dividing both sides by -16, we have:
t^2 = (-64) / (-16)
t^2 = 4
Taking the square root of both sides, we find:
t = ±√4
t = ±2
Since time cannot be negative in this context, we only consider the positive value. Therefore, t = 2.
So, the height of the ball is less than 17 feet during the time interval from t = 0 to t = 2 seconds.
Explanation: