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

1 answer

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.