A ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the function h = -16t^2+ 24t+ 7. In how many seconds does the ball reach its maximum height? round to the nearest hundredth if necessary what is the ball is maximum height
To find the time at which the ball reaches its maximum height, we need to determine the vertex of the parabolic function h = -16t^2 + 24t + 7.
The vertex of a parabola in the form y = ax^2 + bx + c is given by the formula t = -b / (2a).
For our function h = -16t^2 + 24t + 7, we have a = -16 and b = 24.
t = -24 / (2 * -16)
t = -24 / -32
t = 0.75
The ball reaches its maximum height 0.75 seconds after being thrown.
To find the maximum height, we substitute this time value back into the function:
h = -16(0.75)^2 + 24(0.75) + 7
h = -16(0.5625) + 18 + 7
h = -9 + 18 + 7
h = 16 feet
Therefore, the ball reaches its maximum height after 0.75 seconds, and the maximum height is 16 feet.